Andrew Snowden : Syzygies of Segre embeddings

Posted by , part of the Algebraic Geometry Seminar.

At

April 5, 2011, 2:30 p.m.

In

SEO 1227

Abstract

The Segre embedding is the natural embedding of a product of projective spaces into a single projective space. Despite the fundamental nature of this map, its syzygies are not very well understood. I will explain how, by considering all Segre embeddings simultaneously, the spaces of pth syzygies can be given certain structure, and that this structure is finitely generated in a reasonable sense. This implies that there are only finitely many "forms" of pth syzygies. Also, from this finiteness result we deduce that a certain generating function, which records essentially all the information about the pth syzygies of all Segre embeddings, is rational.