View source for Math 763 -- Algebraic Geometry I


=Fall 2019=

== Homework assignments ==

* [[Media:math763hw1.pdf|Homework 1]], due Thursday, September 19th.
* [[Media:math763hw2.pdf|Homework 2]], due Thursday, September 26th.
* [[Media:math763hw3.pdf|Homework 3]], due Tuesday, October 8th.
* [[Media:math763hw4.pdf|Homework 4]], due Thursday, October 17th.
* [[Media:math763hw5.pdf|Homework 5]], due Thursday, October 31st.
* [[Media:math763hw6.pdf|Homework 6]], due Thursday, November 7th.
* [[Media:math763hw7.pdf|Homework 7]], due Thursday, November 14th.
* [[Media:math763hw8.pdf|Homework 8]], due Thursday, November 21st.
* [[Media:math763hw9.pdf|Homework 9]], due Thursday, December 5th.

== 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 [[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.

== Handouts ==

* [[Media:IV.pdf | Correspondence between sets and ideals]]
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]]

== References ==
* Shafarevich, Basic Algebraic Geometry.
* [http://www.jmilne.org/math/CourseNotes/ag.html 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 [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 are [[Media:notes.pdf | 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 [[Math 763 -- Algebraic Geometry I -- Homeworks|homework assignments]], but no exams in this course.