Symplectic desingularization of moduli space of sheaves on a K3 surface

Details Symplectic desingularization of moduli space of sheaves on a K3 surface Symplectic desingularization of moduli space of sheaves on a K3 surface

2004-04-26

arxiv.org/abs/math/0404453v1

Mathematics

Algebraic Geometry

Scientific paper

Let $X$ be a projective K3 surface with generic polarization $\cO_X(1)$ and let $M_c=M(2,0,c)$ be the moduli space of semistable torsion-free sheaves on $X$ of rank 2, with Chern classes $c_1=0$ and $c_2=c$. When $c=2n\ge 4$ is even, $M_c$ is a singular projective variety. We show that there is no symplectic desingularization of $M_{2n}$ if $\frac{n a_n}{2n-3}$ is not an integer where $a_n$ is the Euler number of the Hilbert scheme $X^{[n]}$ of $n$ points in $X$.

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