Xiaolei Zhao (Northeastern), Birational geometry of moduli spaces of sheaves on the projective plane via wall-crossing
In this talk, I will explain how to use Bridgeland stability to study the birational geometry of moduli spaces of sheaves on the projective plane. I will show that wall-crossing naturally provides smooth projective birational models of these moduli spaces, and induces the MMP for them. Moreover a numerical criterion of potential walls being actual walls will be given, and used to compute several cones of these moduli spaces. If time permits, I will also discuss a generalization to non-commutative projective planes, and an application to the study of linear series on these moduli. This talk is based on a series of joint works with Chunyi Li.