Science China Mathematics

, Volume 58, Issue 3, pp 487–500 | Cite as

The geometry of the moduli space of one-dimensional sheaves

Articles
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Abstract

Let M d be the moduli space of stable sheaves on ℙ2 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.

Keywords

effective cone nef cone birational morphism determinant line bundle Bridgeland wall-crossing 

MSC(2010)

14E30 
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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of MathematicsKorea Institute for Advanced StudySeoulKorea

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