Math 245A Topics in algebraic geometry: Introduction to intersection theory in algebraic geometry

Office hours: By appointment, in 380-383M (third floor of the math building). I'll usually be in Mondays and Wednesdays 2:15-3 (my 210A office hours). I will almost always be available to talk at length after each class, and at other times of the week as well.

Our goal: We'll develop intersection theory in algebro-geometric context, which will allow us to deal with singular spaces. In Intersection theory, Fulton develops a very powerful machine quite cleanly and quickly. He requires a reasonable comfort level with schemes. If you haven't seen them before and are ambitious, you should be able to follow the class. (This will involve chatting with me about any points you find confusing.) The technical tools are developed in the first eight or so chapters. The remaining chapters are important applications, and can be read in almost any order once the basic theory is developed. I would like to cover the first 8 chapters (including Chern classes, and intersection theory on nonsingular varieties), and then (in some order) Chapters 9 (excess and residual intersection), 14 (degeneracy loci and Grassmannians), and 15 (Riemann-Roch for nonsingular varieties); most likely we'll settle for less.

Reference: Fulton's Intersection theory (either edition). It will be very helpful if you have a copy.

Homework: Unlike most advanced graduate courses, there likely will be homework. If there is any, it won't be onerous; your main task will be to understand the subject.

Notes: Notes for many of the classes in ps and pdf formats will be posted here. They are very rough, some rougher than others! For the most part I will be following Fulton (with some additional explanation), and I make no claim of originality. (If the pdf file looks funny on your computer or printer, please let me know, so I can try to fix it!) Thanks to Justin Walker for many improvements.