Bridgeland stability conditions and birational geometry of moduli spaces

Prof. A. Bayer (University of Connecticut)

Monday 1st October, 2012 15:30-16:30 214

Abstract

I will explain how to use wall-crossing for Bridgeland stability conditions to systematically study the birational geometry of a moduli space M of sheaves on a K3 surface. It turns out that every birational of M appears as a moduli space of Bridgeland stable objects. Among our applications we obtain a description of the nef cone of M, and we can prove a conjecture on the existence of Lagrangian fibrations due to Hassett-Tschinkel/Huybrechts/Sawon. These results are new even for the Hilbert scheme of points on a generic algebraic K3 surface. This is based on joint work with E. Macri.

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