Commutative Algebra Seminar

A long standing problem in algebraic geometry and commutative algebra is to determine whether every irreducible curve in projective three-space is a set-theoretic complete intersection. One way to approach this problem is via the study of local cohomology modules. As modules over the ring, local cohomology modules are huge (neither finitely generated nor Artinian), hence intractable. However, as modules over the Weil algebra D they can be filtered by simple objects and become manageable. Hence an important task is to understand the D-module structure of local cohomology modules. In this talk we describe their composition series. This is joint work with Robin Hartshorne. Time permitting I would like to talk about two generalizations of this work, one done by Wenliang Zhang and Nicholas Switala, and one by Gennady Lyubeznik. Speaker(s): Claudia Polini (University of Notre Dame)