Mathematical Research Letters

Volume 4 (1997)

Number 2

Desingularization of singular hyperkähler varieties I

Pages: 259 – 271

DOI: http://dx.doi.org/10.4310/MRL.1997.v4.n2.a7

Author

Misha Verbitsky (Institute for Advanced Study)

Abstract

Let $M$ be a singular hyperkähler variety, obtained as a moduli space of stable holomorphic bundles on a compact hyperkähler manifold (alg-geom/9307008). Consider $M$ as a complex variety in one of the complex structures induced by the hyperkähler structure. We show that normalization of $M$ is smooth, hyperkähler and does not depend on the choice of induced complex structure.

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