MOS

Abstract

Kirwan's partial desingularization is a sequence of blow-ups which systematically resolves the strictly semistable points in geometric invariant theory. In this talk, I will discuss various examples of moduli spaces constructed by Kirwan blow-ups such as the moduli space of stable maps of degree 2, the moduli space of Hecke curves and the moduli space of weighted pointed rational curves. If time permits, I will also talk about a joint project with Jun Li in which we study wall crossing and (generalized) Donaldson-Thomas type invariants by using Kirwan blow-ups.