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http://dx.doi.org/10.4134/JKMS.2007.44.1.035

NONEXISTENCE OF A CREPANT RESOLUTION OF SOME MODULI SPACES OF SHEAVES ON A K3 SURFACE  

Choy, Jae-Yoo (Department of Mathematics Seoul National University)
Kiem, Young-Hoon (Department of Mathematics Seoul National University)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.1, 2007 , pp. 35-54 More about this Journal
Abstract
Let $M_c$ = M(2, 0, c) be the moduli space of O(l)-semistable rank 2 torsion-free sheaves with Chern classes $c_1=0\;and\;c_2=c$ on a K3 surface X, where O(1) is a generic ample line bundle on X. When $c=2n\geq4$ is even, $M_c$ is a singular projective variety equipped with a holomorphic symplectic structure on the smooth locus. In particular, $M_c$ has trivial canonical divisor. In [22], O'Grady asks if there is any symplectic desingularization of $M_{2n}$ for $n\geq3$. In this paper, we show that there is no crepant resolution of $M_{2n}$ for $n\geq3$. This obviously implies that there is no symplectic desingularization.
Keywords
crepant resolution; irreducible symplectic variety; moduli space; sheaf; K3 surface; desingularization; Hodge-Deligne polynomial; Poincare polynomial; stringy E-function;
Citations & Related Records

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