The geometry of the moduli space of one-dimensional sheaves

Abstract

Let M-d be the moduli space of stable sheaves on P-2 with Hilbert polynomial dm+1. In this paper, we determine the effective and the nef cone of the space 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 M-6. As a byproduct, we obtain the Betti numbers of the moduli spaces, which confirm the prediction in physics.