Birational models of the Hilbert Scheme of Points in $P^2$ as Moduli of Bridgeland-stable Objects

Birational models of the Hilbert Scheme of Points in $P^2$ as Moduli of Bridgeland-stable Objects

Tue, 07/06/2011
15:45 		Aaron Bertram (Utah) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Birational models of the Hilbert Scheme of Points in $ P^2 $ as Moduli of Bridgeland-stable Objects
The effective cone of the Hilbert scheme of points in $ P^2 $ has finitely many chambers corresponding to finitely many birational models. In this talk, I will identify these models with moduli of Bridgeland-stable two-term complexes in the derived category of coherent sheaves on $ P^2 $ and describe a map from (a slice of) the stability manifold of $ P^2 $ to the effective cone of the Hilbert scheme that would explain the correspondence. This is joint work with Daniele Arcara and Izzet Coskun.