Irena Peeva : Hilbert schemes

Posted by , part of the Departmental Colloquium.

At

April 28, 2006, 2 p.m.

In

SEO 636

Abstract

The Hilbert function is an invariant which measures the size of a graded ideal in a polynomial ring: in particular, it gives the dimension and the multiplicity of the variety defined by a prime ideal. This talk will focus on the properties of ideals with a fixed Hilbert function, starting from classical results of Hilbert, Macaulay, and Grothendieck. The Hilbert scheme (introduced by Grothendieck) parameterizes ideals with a fixed Hilbert function. The talk will discuss properties of Hilbert schemes.