Math 763 -- Algebraic Geometry I: Difference between revisions
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=Fall 2019= | =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 == | == Course description == | ||
| Line 19: | Line 29: | ||
== Handouts == | == Handouts == | ||
* [[Media:IV.pdf|Correspondence between sets and ideals]] | * [[Media:IV.pdf | Correspondence between sets and ideals]] | ||
* [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]] | * [[Media:Nullstellensatz.pdf|Proof of the Nullstellensatz]] | ||
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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. | ||
* Here are [[Media:notes.pdf|notes]] from the last time I taught this course. These were taken in class, so | * Here are [[Media:notes.pdf | notes]] from the last time I taught this course. These were taken in class, so | ||
there are probably typos. | there are probably typos. | ||
Latest revision as of 22:36, 29 November 2019
Fall 2019
Homework assignments
- Homework 1, due Thursday, September 19th.
- Homework 2, due Thursday, September 26th.
- Homework 3, due Tuesday, October 8th.
- Homework 4, due Thursday, October 17th.
- Homework 5, due Thursday, October 31st.
- Homework 6, due Thursday, November 7th.
- Homework 7, due Thursday, November 14th.
- Homework 8, due Thursday, November 21st.
- 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 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.