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

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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.