Birational models of the Hilbert scheme of points on $P^2$ are moduli of Bridgeland-stable complexes
Seminar Room 1, Newton Institute
The minimal model program applied to the Hilbert scheme of points on $P^2$ yields a series of birational models, followed by a Fano fibration. These birational models are themselves moduli spaces, but not (generally) of sheaves. Rather, they are moduli spaces of Bridgeland-stable objects in the derived category. Moreover, each of them may be identified with moduli of quiver representations of the quiver associated to $P^2$ and each wall-crossing is a GIT wall-crossing for a particular representation. This is joint work with Izzet Coskun and Daniele Arcara.