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Zbl 0869.14006
Nakashima, Tohru
Singularity of the moduli space of stable bundles on surfaces. (English)
[J] Compos. Math. 100, No.2, 125-130 (1996). ISSN 0010-437X; ISSN 1570-5846/e

Let $S$ be a smooth projective surface, $H$ its polarization and $(r,D) \in \bbfZ^+ \times \text {Pic} (S)$. Let $M_H (r,D,c)$ be the moduli of rank $r$ $H$-semi-stable sheaves on $S$ with $\text {det} =D$ and $c_2=c$. The author shows that when $\bbfQ \cdot K_s = \bbfQ \cdot H$, then for sufficiently large $c$, $M_H (r,D,c)$ is a $\bbfQ$-Gorenstein variety.
[Jun Li (Stanford)]

MSC 2000:: *14D20 Algebraic moduli problems
14J60 Vector bundles on surfaces and higher-order varieties
14F05 Sheaves, etc.

Keywords: Gorensteinness of moduli variety; polarization

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