Birational Models of Moduli of Sheaves on Surfaces via the Derived Category

Algebra Seminar
Wednesday, March 11, 2015 - 15:05
1 hour (actually 50 minutes)
Skiles 006
University of Utah
Jacobians aren't particularly interesting from the point of view of the minimal model program, and neither are the moduli spaces of vector bundles on curves. But once we pass to vector bundles of higher rank (or torsion-free sheaves) on surfaces, then the birational geometry becomes very interesting. In this talk, I want to describe some recent results that rely on "tilting" the category of coherent sheaves on a surface to produce birational models of moduli that are themselves moduli spaces that come up naturally in the minimal model program.