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arXiv · 1203.0316

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

Daniele Arcara·Aaron Bertram·Izzet Coskun·Jack Huizenga
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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.

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Daniele Arcara, Aaron Bertram, Izzet Coskun, Jack Huizenga. 2012-03-01. The Minimal Model Program for the Hilbert Scheme of Points on P^2 and Bridgeland Stability. https://arxiv.org/abs/1203.0316

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