Mathematical Research Letters

Volume 4, Issue 2, March 1997 pp. 259-271.

Desingularization of singular hyperkähler varieties I

Authors: Misha Verbitsky
Author institution: Institute for Advanced Study

Summary: 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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