Difference between revisions of "Math 763 -- Algebraic Geometry I"

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(Created page with " =Fall 2019= Homework assignments == Course description == This is a first course in algebraic geometry. While there are n...")
 
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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.
 
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.
  
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== Handouts ==
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* [[Media:IV.pdf|Correspondence between sets and ideals]]
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* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]
  
 
== References ==
 
== References ==
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* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).
 
* Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).
 
* 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.
 
* 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.
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* Here are [[Media:notes.pdf|notes]] from the last time I taught this course. These were taken in class, so
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there are probably typos.
  
 
== Information for students ==
 
== Information for students ==

Revision as of 08:30, 10 September 2019

Fall 2019

Homework assignments

Course description

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):

  • Affine and projective varieties.
  • Morphisms and rational maps.
  • Local properties: smoothness and dimension. Tangent space.
  • Divisors.
  • Low-dimensional varieties: curves and surfaces. Blow-ups.
  • The Riemann-Roch Theorem.

Here is a more detailed lecture-by-lecture list of topics that I covered in the past, of course, this is all subject to change.

Handouts

References

  • Shafarevich, Basic Algebraic Geometry.
  • Algebraic Geometry (online notes) by Milne.
  • Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).
  • Here is a discussion on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.
  • Here are notes from the last time I taught this course. These were taken in class, so

there are probably typos.

Information for students

  • Instructor: Dima Arinkin
  • Office Hours: Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603
  • Lectures: TuTh 11am-12:15pm, VV B129
  • Grade: There will be weekly homework assignments, but no exams in this course.