Math 763 -- Algebraic Geometry I
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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.