This is a graduate level introduction to algebraic geometry, both for students who will specialize in a field that uses algebraic geometry as well as students specializing in other fields who are broadening their studies with algebra.
There is no prerequisite course, but it is assumed that students are, minimally, familiar with rings, ideals, quotient rings and the isomorphism theorems as well as prime and maximal ideals. I recommend doing the first reading listed and working on the first problem set, "Homework 0" in advance of the start of the course. Students with a lighter background in algebra will find this to be useful preparation.
The first reading listed, Ch. 0-2 of Commutative Algebra, covers material on ideals and affine varieties. Some of the material on ideals may be unfamiliar to students who are sufficiently prepared for the course, but should be accessible with study. The proof of Zorn's lemma in this reading will not be used, but that result will be applied. Affine varieties (which I do not assume students have seen before) will be covered in lecture, but digesting their correspondence with algebra takes time, and students generally find it beneficial to begin this process early with reading in advance.
| Date | Subject | Reading |
|---|---|---|
| Sept 4 | Introduction | Commutative Algebra Ch. 0-2 |
| Sept 6 |