Lawrence Ein, U. Illinois, Chicago, USA

Hyperbolicity and Weil-Petersson geometry

Abstract

We discussed joint work with Rob Lazarsfeld. We'll describe how to use Hilbert schemes of points to study syzygies. In particular we are able to solve a conjecture of Green and Lazarsfeld which says that one detects the gonality of an algebraic curve from the Betti numbers of  a minimal resolution of the coordinate ring of a sufficiently ample line bundle on the curve. We also discuss the generalization of the theorem to higher dimensions.