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The minimal model program for the Hilbert scheme of points on P-2 and Bridgeland stability
journal contributionposted on 2013-12-03, 00:00 authored by Daniele Arcara, Aaron Bertram, Izzet Coskun, Jack Huizenga
In 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.
During the preparation of this article the second author was partially supported by the NSF grant DMS-0901128. The third author was partially supported by the NSF grant DMS-0737581, NSF CAREER grant 0950951535, and an Arthur P. Sloan Foundation Fellowship. The fourth author was partially supported by an NSF Graduate Research Fellowship.
Publisher StatementNOTICE: This is the author’s version of a work that was accepted for publication in Advances in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in Mathematics, [Vol 235, 2013] DOI: 10.1016/j.aim.2012.11.018