Difference between revisions of "Math 763 -- Algebraic Geometry I"
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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. | ||
+ | == Handouts == | ||
+ | |||
+ | * [[Media:IV.pdf|Correspondence between sets and ideals]] | ||
+ | * [[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. | ||
+ | * 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 == | == Information for students == |
Revision as of 08:30, 10 September 2019
Contents
Fall 2019
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.