Birational models of moduli spaces of coherent sheaves on the projective plane

Abstract

We study the birational geometry of moduli spaces of semistable sheaves on\nthe projective plane via Bridgeland stability conditions. We show that the\nentire MMP of their moduli spaces can be run via wall-crossing. Via a\ndescription of the walls, we give a numerical description of their movable\ncones, along with its chamber decomposition corresponding to minimal models. As\nan application, we show that for primitive vectors, all birational models\ncorresponding to open chambers in the movable cone are smooth and irreducible.\n