Abstract:
In these lectures, I will discuss recent developments in the birational geometry of moduli spaces of sheaves on surfaces motivated by Bridgeland stability conditions. My emphasis will be on concrete examples. After reviewing the basic facts about Hilbert schemes of points and moduli spaces of vector bundles on surfaces, I will introduce Bridgeland stability conditions. I will then describe joint work with Arcara, Bertram and Huizenga on the birational geometry of Hilbert schemes of points on the projective plane. Building from there, I will discuss recent joint work with Huizenga on computing nef cones of moduli spaces of sheaves on surfaces, often using the projective plane as the motivating example.

info: http://ricerca.mat.uniroma3.it/users/geometria/Sunti/coskun.html