Difference between revisions of "Math 764 -- Algebraic Geometry II"

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=Spring 2019=
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== Course description ==
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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.
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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.
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== References ==
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* Hartshorne, Algebraic Geometry.
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* Shafarevich, Basic Algebraic Geometry.
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* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].
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* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.
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== Information for students ==
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* '''Instructor''': Dima Arinkin
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* '''Office Hours''': Monday 2-3pm and by appointment in VV 603
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* '''Lectures''': MWF 9:55-10:45am, VV B131
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* '''Grade''': There will be weekly homework assignments, but no exams in this course.
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=Spring 2017=
 
=Spring 2017=
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* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].
 
* Ravi Vakil’s online notes, [http://math.stanford.edu/~vakil/216blog/FOAGdec2915public.pdf The Rising Sea].
 
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.
 
* [[Media:Math863Spring2015.pdf|Notes]] by Daniel Hast for this course (Algebraic Geometry II) in 2015.
 
== Information for students ==
 
 
* '''Instructor''': Dima Arinkin
 
* '''Office Hours''': Monday 3-4pm, Friday 11-11:45am, and by appointment in VV 603
 
* '''Lectures''': MWF 12:05-12:55pm, VV B321
 
* '''Grade''': There will be weekly [[Math 764 -- Algebraic Geometry II -- Homeworks|homework assignments]], but no exams in this course.
 

Revision as of 09:08, 22 January 2020

Spring 2019

Course description

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.

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.

References

  • Hartshorne, Algebraic Geometry.
  • Shafarevich, Basic Algebraic Geometry.
  • Ravi Vakil’s online notes, The Rising Sea.
  • Notes by Daniel Hast for this course (Algebraic Geometry II) in 2015.

Information for students

  • Instructor: Dima Arinkin
  • Office Hours: Monday 2-3pm and by appointment in VV 603
  • Lectures: MWF 9:55-10:45am, VV B131
  • Grade: There will be weekly homework assignments, but no exams in this course.


Spring 2017

Homework assignments

Course description

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.

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.

References

  • Hartshorne, Algebraic Geometry.
  • Shafarevich, Basic Algebraic Geometry.
  • Ravi Vakil’s online notes, The Rising Sea.
  • Notes by Daniel Hast for this course (Algebraic Geometry II) in 2015.