The minimal model program for deformations of Hilbert schemes of points on the projective plane

Abstract

We study the birational geometry of deformations of Hilbert schemes of points on P 2 . We show that moduli of Bridgeland-stable objects are smooth, irreducible, projective varieties, which are birationally equivalent to these deformations. Moreover, wall crossing in the space of Bridgeland-stability conditions induces the minimal model program for these deformations. In particular, for Hilbert schemes of points on P 2 , this proves a correspondence between destabilizing walls in the space of Bridgeland-stability conditions and stable base locus walls in the effective divisor cone, conjectured by Arcara,