The geometry of the moduli space of one-dimensional sheaves

Abstract

Let ${\mathbf{M}}_d$ be the moduli space of stable sheaves on ${\mathbb{P}}^2$ with Hilbert polynomial $dm+1$. In this paper, we determine the effective and the nef cone of the space ${\mathbf{M}}_d$ by natural geometric divisors. Main idea is to use the wall-crossing on the space of Bridgeland stability conditions and to compute the intersection numbers of divisors with curves by using the Grothendieck-Riemann-Roch theorem. We also present the stable base locus decomposition of the space ${\mathbf{M}}_6$. As a byproduct, we obtain the Betti numbers of the moduli spaces, which confirm the prediction in physics.

Typos corrected. To appear in Science China Mathematics

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• The Omega deformed B-model for rigid N=2 theories
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• The refined BPS index from stable pair invariants
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Cited by in corpus (1)

• Moduli of sheaves, Fourier-Mukai transform, and partial desingularization