Algebraic Geometry Seminar
Andrew Snowden
MIT
Syzygies of Segre embeddings
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.
Tuesday April 5, 2011 at 2:30 PM in SEO 1227