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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 Chernclasses c_1(F) = 0, c_2(F) = 2n is a singular projective variety, endowed witha holomorphic symplectic structure on the smooth locus. In this paper, we showthat there does not exist a crepant resolution of M(2; 0; 2n) for n>1. Thiscertainly implies that there is no symplectic desingularization of M(2, 0, 2n)for n>1.

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