Birational models of Hilb_n(P2) as moduli of Bridgeland-stable objects

Following Bridgeland, I'll describe a two-parameter family of stability conditions on the derived category of coherent sheaves on the projective plane. Fixing the Chern classes of the ideal sheaf of n points in the plane imposes a wall and chamber structure, with the property that in one chamber the moduli of stable objects with invariants (1,0,-n) is the Hilbert scheme. In this talk, I will identify the other chambers and describe a map from the family of stability conditions to the cone of effective divisors on Hilb_n(P2) that matches (in all cases we've been able to compute) Bridgeland walls with walls in the effective cone. This is joint work with Daniele Arcara and Izzet Coskun.