The Minimal Model Program for the Hilbert Scheme of Points on P^2 and Bridgeland Stability

Abstract

In this paper, we study the birational geometry of the Hilbert scheme 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 at most 9, we explicitly determine the walls in both interpretations and describe the corresponding flips and divisorial contractions.

42 pages

References in corpus (3)

• Markov convexity and local rigidity of distorted metrics
• Computing the Walls Associated to Bridgeland Stability Conditions on Projective Surfaces
• Restrictions of Steiner bundles and divisors on the Hilbert scheme of points in the plane

Cited by in corpus (8)

• A generalized Bogomolov-Gieseker inequality for the three-dimensional projective space
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• Projectivity and Birational Geometry of Bridgeland moduli spaces
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• Stability conditions and extremal contractions
• The geometry of the moduli space of one-dimensional sheaves
• On the birational geometry of the parameter space for codimension 2 complete intersections
• Virtual Poincaré polynomial of the space of stable pairs supported on quintic curves