The Minimal Model Program for the Hilbert Scheme of Points on P² and Bridgeland Stability

2012/03/01 by Arcara, Daniele, Bertram, Aaron, Coskun, Izzet +1 · 6 citations
#14C05 #14D20 #14D23 #14E30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.0316

Abstract

In this paper, we study the birational geometry of the Hilbert scheme of n points on P². 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.

Cited by

• Stability conditions on products of curves and Hilbert schemes of surfaces
• Stability conditions for coherent systems on Integral Curves
• Extremal divisors in the Hilbert scheme of points on ℙ² are preserved under residuality
• Nef cones of Hilbert schemes of points on some K3 surfaces
• A proof of the Briançon-Iarrobino Conjecture in three dimensions
• Moduli of non-pure sheaves and contractions of Hilbert schemes

Related

• Projectivity and Birational Geometry of Bridgeland moduli spaces
• The MMP for deformations of Hilbert schemes of points on the projective plane
• Variation of stability for moduli spaces of unordered points in the plane
• Moduli of Bridgeland semistable objects on ℙ²
• Birational geometry of moduli spaces of sheaves and Bridgeland stability