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Download fileThe minimal model program for the Hilbert scheme of points on P-2 and Bridgeland stability
journal contribution
posted on 2013-12-03, 00:00 authored by Daniele Arcara, Aaron Bertram, Izzet Coskun, Jack HuizengaIn this paper, we study the birational geometry of the Hilbert scheme P-2[n] of n-points on P-2. We discuss the stable base locus decomposition of the effective cone and the corresponding birational models. We give modular interpretations to the models in terms of moduli spaces of Bridgeland semi-stable objects. We construct these moduli spaces as moduli spaces of quiver representations using G.I.T. and thus show that they are projective. There is a precise correspondence between wall-crossings in the Bridgeland stability manifold and wall-crossings between Mori cones. For n <= 9, we explicitly determine the walls in both interpretations and describe the corresponding flips and divisorial contractions.