DMM seminar

Speaker: Arend Bayer (Edinburgh)
Title: Birational geometry of moduli of sheaves on K3s via Bridgeland stability
Date (JST): Mon, Jan 21, 2013, 14:00 - 17:00
Place: Seminar Room B
Abstract: I will explain recent results with Emanuele Macrì, in which we use wall-crossing for Bridgeland stabiltiy conditions to systematically study the birational geometry of moduli of sheaves on K3 surfaces. In particular, we obtain descriptions of their nef conyes via the Mukai lattice of the K3, their moveable cones, their divisorial contractions, and obtain counter-examples to various conjectures in the literature. We also give a proof of the Lagrangian fibration conjecture (due to Hassett-Tschinkel/Huybrechts/Sawon) via wall-crossing. These results are new even for Hilbert schemes on the quartic surface in P^3.

Our method is based on a natural map from the space of stability conditions to the movable cone of the moduli space. This connects wall-crossing with the MMP (minimal model program) of the moduli space.
Remarks: Break 15:00-15:30