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On the existence of a crepant resolution of some moduli spaces of sheaves on an abelian surface

Jaeyoo Choy·Young-Hoon Kiem
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Abstract

Let J be an abelian surface with a generic ample line bundle O(1). For n>0, the moduli space M(2, 0, 2n) of O(1)-semistable sheaves F of rank 2 with Chern classes c_1(F) = 0, c_2(F) = 2n is a singular projective variety, endowed with a holomorphic symplectic structure on the smooth locus. In this paper, we show that there does not exist a crepant resolution of M(2; 0; 2n) for n>1. This certainly implies that there is no symplectic desingularization of M(2, 0, 2n) for n>1.

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Jaeyoo Choy, Young-Hoon Kiem. 2005-05-12. On the existence of a crepant resolution of some moduli spaces of sheaves on an abelian surface. https://arxiv.org/abs/math/0505239

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