Jack Huizenga : Higher rank interpolation problems and Bridgeland stability

Posted by Jack Huizenga , part of the Algebraic Geometry Seminar.

At

May 1, 2013, 4 p.m.

In

SEO 427

Abstract

A fundamental problem in algebraic geometry is to determine when a zero-dimensional subscheme of a variety imposes independent conditions on sections of a line bundle. More generally, one can consider when a scheme imposes independent conditions on sections of a vector bundle. Studying such questions amounts to studying the birational geometry of Hilbert schemes of points, or base loci of theta divisors on moduli spaces of sheaves. We will discuss how Bridgeland stability gives a natural way of decomposing the ideal sheaf of a zero-scheme which helps solve the higher rank interpolation problem.