Birational models of moduli spaces of coherent sheaves on the projective plane

Abstract

We study the birational geometry of moduli spaces of semistable sheaves on the projective plane via Bridgeland stability conditions. We show that the entire MMP of their moduli spaces can be run via wall-crossing. Via a description of the walls, we give a numerical description of their movable cones, along with its chamber decomposition corresponding to minimal models. As an application, we show that for primitive vectors, all birational models corresponding to open chambers in the movable cone are smooth and irreducible.

arXiv comment62 pages, 13 figures, comments are welcome

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Cited by in corpus (20)

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• Scattering diagrams, stability conditions, and coherent sheaves on ${\mathbb{P}}^2$
• Stability conditions on threefolds with nef tangent bundles
• Some remarks on Fano threefolds of index two and stability conditions
• The Effective Cone of Moduli Spaces of Sheaves on a Smooth Quadric Surface
• BPS Dendroscopy on Local $P^2$
• Stability and Applications
• Higher rank Clifford indices of curves on a K3 surface
• Fourier-Mukai transforms and stable sheaves on Weierstrass elliptic surfaces
• Nef divisors for moduli spaces of complexes with compact support
• Contractibility of space of stability conditions on the projective plane via global dimension function
• The cohomology of general tensor products of vector bundles on the projective plane
• Stable sheaves on bielliptic surfaces: from the classical to the modern
• Strange duality on ${\mathbb{P}}^2$ via quiver representations
• On the birational geometry of Hilbert schemes of points and Severi divisors
• Birational geometry of moduli spaces of sheaves and Bridgeland stability
• Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces
• Bridgeland wall-crossing for some Simpson moduli spaces on ${\mathbb{P}}^1\times {\mathbb{P}}^1$
• Wall-Crossing implies Brill-Noether. Applications of stability conditions on surfaces
• Minimal free resolutions of sheaves on the projective plane and the stable base locus decomposition of their moduli spaces