MATH 767 — Fall 1999
Algebraic Geometry

Instructor: Mike Stillman

Time: TR 11:40-12:55

Room: Malott 206

This course is a first graduate course in algebraic geometry. The plan is to introduce the main techniques of algebraic geometry: divisors, sheaves, cohomology, intersection theory, in the context of examples and working towards the classification of surfaces. Many examples will be given, and the approach we will use towards the classification parallels (but is much simpler than) the recent approaches to classification of three-folds and higher dimensional varieties.

We will state without proof several useful tools (we will prove a lot as well!), and will concentrate on using these methods. I feel that this is important for motivation.

Textbook: I will mostly follow "Chapters on Algebraic Surfaces" by Miles Reid. This is the first part of the book "Complex Algebraic Geometry", edited by J. Kollar, and published by the AMS, 1997. (ISBN 0-8218-0432-4).

Prerequisites: A course in undergraduate algebraic geometry, as in the first chapter of Hartshorne, the undergraduate algebraic geometry book by Miles Reid, the first three chapters of Shafarevich, or the book by Cox, Little and O'Shea.

Homework: It is important to do mathematics, and not just see it. Therefore, I will hand out problems every two weeks. Students will also be encouraged to investigate examples by computer (using Macaulay2, or some other computer algebra system).

Last modified: April 7, 2003