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arXiv · 1311.0134

The geometry of the moduli space of one-dimensional sheaves

Jinwon Choi·Kiryong Chung
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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.

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Jinwon Choi, Kiryong Chung. 2014-10-27. The geometry of the moduli space of one-dimensional sheaves. https://arxiv.org/abs/1311.0134

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