Math 767 — Algebraic Geometry

Spring 2003

Instructor: Irena Peeva

Time: TR 1:25-2:40

Room: MT 205

Topic: Free Resolutions

Prerequisites: MATH 631

The structure of a finitely generated R-module (where R is a polynomial ring or a quotient of a polynomial ring) can be described by a free resolution. This idea was introduced by Hilbert in two of his papers. In essence, constructing a free resolution consists of solving systems of R-linear equations.

Topics to be covered:

1. introduction to free resolutions
2. resolutions and toric varieties
3. monomial resolutions
4. resolutions over complete intersections
5. resolutions in algebraic geometry

Many open problems and conjectures will be discussed.

Last modified: April 7, 2003