Tim Ryan : Minimal free resolutions and birational geometry of moduli spaces of sheaves

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

Sept. 20, 2021, 3 p.m.

In

Zoom

Abstract

Recent work on the birational geometry of moduli spaces has largely worked along two lines; either it has used the machinery of Bridgeland stability conditions or it has solved the interpolation problems for vector bundles. In this talk, I will discuss recent work with Manuel Leal and Cesar Lozano Huerta in which we connect these approaches to the minimal free resolutions of sheaves. In particular, I will show that the base locus of (primary) extremal chamber of the effective cone of a moduli space of sheaves on the projective plane can be characterized in terms of the map in the Gaeta minimal free resolution. Time permitting, I will discuss a conjecture for the exact relationship between the minimal free resolution, Bridgeland destabilizing objects, and the stable base locus decomposition.