https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Arinkin&feedformat=atomUW-Math Wiki - User contributions [en]2020-07-07T10:15:25ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=File:Math764hw10.pdf&diff=19383File:Math764hw10.pdf2020-04-26T20:06:31Z<p>Arinkin: Arinkin uploaded a new version of File:Math764hw10.pdf</p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19382Math 764 -- Algebraic Geometry II2020-04-26T20:05:53Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
* [[Media:math764hw3.pdf|Homework 3]], due Wednesday, February 26th.<br />
* [[Media:math764hw4.pdf|Homework 4]], due Wednesday, March 4th.<br />
* [[Media:math764hw5.pdf|Homework 5]], due Wednesday, March 25th.<br />
* [[Media:math764hw6.pdf|Homework 6]], due Wednesday, April 1st.<br />
* [[Media:math764hw7.pdf|Homework 7]], due Wednesday, April 8th.<br />
* [[Media:math764hw8.pdf|Homework 8]], due Wednesday, April 15th.<br />
* [[Media:math764hw9.pdf|Homework 9]], due Wednesday, April 22nd.<br />
* [[Media:math764hw10.pdf|Homework 10]] (and last), due Wednesday, April 29th (corrected conventions of Galois twist).<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math764hw10.pdf&diff=19381File:Math764hw10.pdf2020-04-23T19:18:09Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19380Math 764 -- Algebraic Geometry II2020-04-23T19:17:54Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
* [[Media:math764hw3.pdf|Homework 3]], due Wednesday, February 26th.<br />
* [[Media:math764hw4.pdf|Homework 4]], due Wednesday, March 4th.<br />
* [[Media:math764hw5.pdf|Homework 5]], due Wednesday, March 25th.<br />
* [[Media:math764hw6.pdf|Homework 6]], due Wednesday, April 1st.<br />
* [[Media:math764hw7.pdf|Homework 7]], due Wednesday, April 8th.<br />
* [[Media:math764hw8.pdf|Homework 8]], due Wednesday, April 15th.<br />
* [[Media:math764hw9.pdf|Homework 9]], due Wednesday, April 22nd.<br />
* [[Media:math764hw10.pdf|Homework 10]] (and last), due Wednesday, April 29th.<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math764hw9.pdf&diff=19359File:Math764hw9.pdf2020-04-16T18:05:04Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19358Math 764 -- Algebraic Geometry II2020-04-16T18:03:42Z<p>Arinkin: </p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
* [[Media:math764hw3.pdf|Homework 3]], due Wednesday, February 26th.<br />
* [[Media:math764hw4.pdf|Homework 4]], due Wednesday, March 4th.<br />
* [[Media:math764hw5.pdf|Homework 5]], due Wednesday, March 25th.<br />
* [[Media:math764hw6.pdf|Homework 6]], due Wednesday, April 1st.<br />
* [[Media:math764hw7.pdf|Homework 7]], due Wednesday, April 8th.<br />
* [[Media:math764hw8.pdf|Homework 8]], due Wednesday, April 15th.<br />
* [[Media:math764hw9.pdf|Homework 9]], due Wednesday, April 22nd.<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math764hw8.pdf&diff=19346File:Math764hw8.pdf2020-04-09T18:50:17Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19345Math 764 -- Algebraic Geometry II2020-04-09T18:50:01Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
* [[Media:math764hw3.pdf|Homework 3]], due Wednesday, February 26th.<br />
* [[Media:math764hw4.pdf|Homework 4]], due Wednesday, March 4th.<br />
* [[Media:math764hw5.pdf|Homework 5]], due Wednesday, March 25th.<br />
* [[Media:math764hw6.pdf|Homework 6]], due Wednesday, April 1st.<br />
* [[Media:math764hw7.pdf|Homework 7]], due Wednesday, April 8th.<br />
* [[Media:math764hw8.pdf|Homework 8]], due Wednesday, April 15th.<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math764hw7.pdf&diff=19326File:Math764hw7.pdf2020-04-02T02:10:46Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19325Math 764 -- Algebraic Geometry II2020-04-02T02:10:33Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
* [[Media:math764hw3.pdf|Homework 3]], due Wednesday, February 26th.<br />
* [[Media:math764hw4.pdf|Homework 4]], due Wednesday, March 4th.<br />
* [[Media:math764hw5.pdf|Homework 5]], due Wednesday, March 25th.<br />
* [[Media:math764hw6.pdf|Homework 6]], due Wednesday, April 1st.<br />
* [[Media:math764hw7.pdf|Homework 7]], due Wednesday, April 8th.<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19324Math 764 -- Algebraic Geometry II2020-04-02T02:10:19Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
* [[Media:math764hw3.pdf|Homework 3]], due Wednesday, February 26th.<br />
* [[Media:math764hw4.pdf|Homework 4]], due Wednesday, March 4th.<br />
* [[Media:math764hw5.pdf|Homework 5]], due Wednesday, March 25th.<br />
* [[Media:math764hw6.pdf|Homework 6]], due Wednesday, April 1st.<br />
* [[Media:math764hw6.pdf|Homework 7]], due Wednesday, April 8th.<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math764hw6.pdf&diff=19308File:Math764hw6.pdf2020-03-25T23:10:33Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19307Math 764 -- Algebraic Geometry II2020-03-25T22:58:35Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
* [[Media:math764hw3.pdf|Homework 3]], due Wednesday, February 26th.<br />
* [[Media:math764hw4.pdf|Homework 4]], due Wednesday, March 4th.<br />
* [[Media:math764hw5.pdf|Homework 5]], due Wednesday, March 25th.<br />
* [[Media:math764hw6.pdf|Homework 6]], due Wednesday, April 1st.<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math764hw5.pdf&diff=19262File:Math764hw5.pdf2020-03-13T00:06:44Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19261Math 764 -- Algebraic Geometry II2020-03-13T00:06:28Z<p>Arinkin: </p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
* [[Media:math764hw3.pdf|Homework 3]], due Wednesday, February 26th.<br />
* [[Media:math764hw4.pdf|Homework 4]], due Wednesday, March 4th.<br />
* [[Media:math764hw5.pdf|Homework 5]], due Wednesday, March 25th.<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19210Math 764 -- Algebraic Geometry II2020-03-05T23:19:42Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
* [[Media:math764hw3.pdf|Homework 3]], due Wednesday, February 26th.<br />
* [[Media:math764hw4.pdf|Homework 4]], due Wednesday, March 4th.<br />
* Homework 5 will be due after the break: Wednesday, March 25th.<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math764hw4.pdf&diff=19171File:Math764hw4.pdf2020-02-28T21:58:57Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19170Math 764 -- Algebraic Geometry II2020-02-28T21:58:48Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
* [[Media:math764hw3.pdf|Homework 3]], due Wednesday, February 26th.<br />
* [[Media:math764hw4.pdf|Homework 4]], due Wednesday, March 4th.<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math764hw3.pdf&diff=19089File:Math764hw3.pdf2020-02-22T02:31:47Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19088Math 764 -- Algebraic Geometry II2020-02-22T02:31:37Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
* [[Media:math764hw3.pdf|Homework 3]], due Wednesday, February 26th.<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math764hw2.pdf&diff=19015File:Math764hw2.pdf2020-02-13T00:16:26Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=19014Math 764 -- Algebraic Geometry II2020-02-13T00:16:14Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
* [[Media:math764hw2.pdf|Homework 2]], due Wednesday, February 19th.<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math764hw1.pdf&diff=18930File:Math764hw1.pdf2020-02-05T22:21:28Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=18929Math 764 -- Algebraic Geometry II2020-02-05T22:21:11Z<p>Arinkin: </p>
<hr />
<div>=Spring 2020=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math764hw1.pdf|Homework 1]], due Wednesday, February 12th.<br />
<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_764_--_Algebraic_Geometry_II&diff=18734Math 764 -- Algebraic Geometry II2020-01-22T15:08:38Z<p>Arinkin: </p>
<hr />
<div>=Spring 2019=<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes. <br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Monday 2-3pm and by appointment in VV 603<br />
* '''Lectures''': MWF 9:55-10:45am, VV B131<br />
* '''Grade''': There will be weekly homework assignments, but no exams in this course.<br />
<br />
<br />
<br />
=Spring 2017=<br />
<br />
[[Math 764 -- Algebraic Geometry II -- Homeworks|Homework assignments]]<br />
<br />
== Course description ==<br />
<br />
This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.<br />
<br />
In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.<br />
<br />
== References ==<br />
* Hartshorne, Algebraic Geometry.<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].<br />
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw9.pdf&diff=18509File:Math763hw9.pdf2019-11-29T22:36:29Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=18508Math 763 -- Algebraic Geometry I2019-11-29T22:36:13Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.<br />
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.<br />
* [[Media:math763hw3.pdf|Homework 3]], due Tuesday, October 8th.<br />
* [[Media:math763hw4.pdf|Homework 4]], due Thursday, October 17th.<br />
* [[Media:math763hw5.pdf|Homework 5]], due Thursday, October 31st.<br />
* [[Media:math763hw6.pdf|Homework 6]], due Thursday, November 7th.<br />
* [[Media:math763hw7.pdf|Homework 7]], due Thursday, November 14th.<br />
* [[Media:math763hw8.pdf|Homework 8]], due Thursday, November 21st.<br />
* [[Media:math763hw9.pdf|Homework 9]], due Thursday, December 5th.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw8.pdf&diff=18418File:Math763hw8.pdf2019-11-15T05:07:34Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=18417Math 763 -- Algebraic Geometry I2019-11-15T05:06:50Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.<br />
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.<br />
* [[Media:math763hw3.pdf|Homework 3]], due Tuesday, October 8th.<br />
* [[Media:math763hw4.pdf|Homework 4]], due Thursday, October 17th.<br />
* [[Media:math763hw5.pdf|Homework 5]], due Thursday, October 31st.<br />
* [[Media:math763hw6.pdf|Homework 6]], due Thursday, November 7th.<br />
* [[Media:math763hw7.pdf|Homework 7]], due Thursday, November 14th.<br />
* [[Media:math763hw8.pdf|Homework 8]], due Thursday, November 21st.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=18416Math 763 -- Algebraic Geometry I2019-11-15T05:06:38Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.<br />
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.<br />
* [[Media:math763hw3.pdf|Homework 3]], due Tuesday, October 8th.<br />
* [[Media:math763hw4.pdf|Homework 4]], due Thursday, October 17th.<br />
* [[Media:math763hw5.pdf|Homework 5]], due Thursday, October 31st.<br />
* [[Media:math763hw6.pdf|Homework 6]], due Thursday, November 7th.<br />
* [[Media:math763hw7.pdf|Homework 7]], due Thursday, November 14th.<br />
* [[Media:math763hw7.pdf|Homework 8]], due Thursday, November 21st.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw7.pdf&diff=18358File:Math763hw7.pdf2019-11-08T03:41:37Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=18357Math 763 -- Algebraic Geometry I2019-11-08T03:38:59Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.<br />
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.<br />
* [[Media:math763hw3.pdf|Homework 3]], due Tuesday, October 8th.<br />
* [[Media:math763hw4.pdf|Homework 4]], due Thursday, October 17th.<br />
* [[Media:math763hw5.pdf|Homework 5]], due Thursday, October 31st.<br />
* [[Media:math763hw6.pdf|Homework 6]], due Thursday, November 7th.<br />
* [[Media:math763hw7.pdf|Homework 7]], due Thursday, November 14th.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Numbers.pdf&diff=18347File:Numbers.pdf2019-11-06T23:50:09Z<p>Arinkin: Arinkin uploaded a new version of File:Numbers.pdf</p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Numbers.pdf&diff=18345File:Numbers.pdf2019-11-06T22:50:54Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=18344Putnam Club2019-11-06T22:50:35Z<p>Arinkin: /* Fall 2019 */</p>
<hr />
<div><br />
''Organizers: Dima Arinkin, Mihaela Ifrim, Chanwoo kim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
The Virginia Tech Regional Mathematics Contest is on Oct 26, 9:00-11:30am at Van Vleck Hall B123. [https://docs.google.com/forms/d/e/1FAIpQLSfLFgT77SQxbZYN-vQUktsSsekWWITvLf0oiNOYxjCD55oIkg/viewform?usp=sf_link/ Please click this link to register. ]<br />
<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[ODE.pdf | ODE of the first order]] Chanwoo<br />
* November 6: [[Media:Numbers.pdf | Number theory]] Dima<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=18343Putnam Club2019-11-06T22:50:13Z<p>Arinkin: /* Fall 2019 */</p>
<hr />
<div><br />
''Organizers: Dima Arinkin, Mihaela Ifrim, Chanwoo kim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
The Virginia Tech Regional Mathematics Contest is on Oct 26, 9:00-11:30am at Van Vleck Hall B123. [https://docs.google.com/forms/d/e/1FAIpQLSfLFgT77SQxbZYN-vQUktsSsekWWITvLf0oiNOYxjCD55oIkg/viewform?usp=sf_link/ Please click this link to register. ]<br />
<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[ODE.pdf | ODE of the first order]] Chanwoo<br />
* November 6: [[Numbers.pdf | Number theory]] Dima<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw6.pdf&diff=18285File:Math763hw6.pdf2019-10-31T23:15:20Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=18284Math 763 -- Algebraic Geometry I2019-10-31T23:15:08Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.<br />
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.<br />
* [[Media:math763hw3.pdf|Homework 3]], due Tuesday, October 8th.<br />
* [[Media:math763hw4.pdf|Homework 4]], due Thursday, October 17th.<br />
* [[Media:math763hw5.pdf|Homework 5]], due Thursday, October 31st.<br />
* [[Media:math763hw6.pdf|Homework 6]], due Thursday, November 7th.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw5.pdf&diff=18253File:Math763hw5.pdf2019-10-25T19:40:14Z<p>Arinkin: Arinkin uploaded a new version of File:Math763hw5.pdf</p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw5.pdf&diff=18244File:Math763hw5.pdf2019-10-25T01:09:45Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=18243Math 763 -- Algebraic Geometry I2019-10-25T01:09:20Z<p>Arinkin: </p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.<br />
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.<br />
* [[Media:math763hw3.pdf|Homework 3]], due Tuesday, October 8th.<br />
* [[Media:math763hw4.pdf|Homework 4]], due Thursday, October 17th.<br />
* [[Media:math763hw5.pdf|Homework 5]], due Thursday, October 31st.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=18213Math 763 -- Algebraic Geometry I2019-10-18T23:14:52Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.<br />
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.<br />
* [[Media:math763hw3.pdf|Homework 3]], due Tuesday, October 8th.<br />
* [[Media:math763hw4.pdf|Homework 4]], due Thursday, October 17th.<br />
* Homework 5 will be assigned next week (either Tuesday, October 22nd or Thursday, October 24th) and due around Halloween.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw4.pdf&diff=18139File:Math763hw4.pdf2019-10-09T23:21:18Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=18138Math 763 -- Algebraic Geometry I2019-10-09T23:21:07Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.<br />
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.<br />
* [[Media:math763hw3.pdf|Homework 3]], due Tuesday, October 8th.<br />
* [[Media:math763hw4.pdf|Homework 4]], due Thursday, October 17th.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=18099Math 763 -- Algebraic Geometry I2019-10-04T00:02:26Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.<br />
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.<br />
* [[Media:math763hw3.pdf|Homework 3]], due '''Tuesday, October 8th'''.<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=18079Algebra and Algebraic Geometry Seminar Fall 20192019-10-02T00:31:05Z<p>Arinkin: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2019 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Spring 2020 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
<br />
== Fall 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 6<br />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<br />
|-<br />
|September 27<br />
|<br />
|<br />
|<br />
|-<br />
|October 4<br />
|<br />
|<br />
|<br />
|-<br />
|October 11<br />
|<br />
|<br />
|<br />
|-<br />
|October 18<br />
|Kevin Tucker (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|October 25<br />
|Reserved<br />
|<br />
|Dima<br />
|-<br />
|November 1<br />
|Michael Brown<br />
|TBD<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|TBD<br />
|Daniel<br />
|-<br />
|November 15<br />
|<br />
|<br />
|<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<br />
|-<br />
|November 29<br />
| No Seminar<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|RESERVED<br />
|<br />
| Reserved (Matroids Day)<br />
|-<br />
|December 13<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.<br />
<br />
<br />
== Notes ==<br />
Because of exams and/or travel, Daniel is unable to attend seminars on Oct 11, Oct 18, Nov 15, and Dec 13.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=Math_763_--_Algebraic_Geometry_I&diff=18042Math 763 -- Algebraic Geometry I2019-09-27T02:31:16Z<p>Arinkin: /* Homework assignments */</p>
<hr />
<div><br />
=Fall 2019=<br />
<br />
== Homework assignments ==<br />
<br />
* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.<br />
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.<br />
* [[Media:math763hw3.pdf|Homework 3]], due Thursday, October 3rd. (I accidentally uploaded an old version, should be fixed now.)<br />
<br />
== Course description ==<br />
<br />
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):<br />
<br />
* Affine and projective varieties.<br />
* Morphisms and rational maps.<br />
* Local properties: smoothness and dimension. Tangent space.<br />
* Divisors.<br />
* Low-dimensional varieties: curves and surfaces. Blow-ups.<br />
* The Riemann-Roch Theorem.<br />
<br />
Here is a more detailed lecture-by-lecture [[Math 763 -- Algebraic Geometry I -- Detailed list of topics|list of topics]] that I covered in the past, of course, this is all subject to change.<br />
<br />
== Handouts ==<br />
<br />
* [[Media:IV.pdf | Correspondence between sets and ideals]]<br />
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]<br />
<br />
== References ==<br />
* Shafarevich, Basic Algebraic Geometry.<br />
* [http://www.jmilne.org/math/CourseNotes/ag.html Algebraic Geometry] (online notes) by Milne.<br />
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).<br />
* Here is a [https://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne discussion] on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.<br />
* Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so<br />
there are probably typos.<br />
<br />
== Information for students ==<br />
<br />
* '''Instructor''': Dima Arinkin<br />
* '''Office Hours''': Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603<br />
* '''Lectures''': TuTh 11am-12:15pm, VV B129<br />
* '''Grade''': There will be weekly [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.</div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw3.pdf&diff=18041File:Math763hw3.pdf2019-09-27T02:30:06Z<p>Arinkin: Arinkin uploaded a new version of File:Math763hw3.pdf</p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw3.pdf&diff=18040File:Math763hw3.pdf2019-09-27T02:29:27Z<p>Arinkin: Arinkin uploaded a new version of File:Math763hw3.pdf</p>
<hr />
<div></div>Arinkinhttps://www.math.wisc.edu/wiki/index.php?title=File:Math763hw3.pdf&diff=18039File:Math763hw3.pdf2019-09-26T23:58:53Z<p>Arinkin: </p>
<hr />
<div></div>Arinkin