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.