Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 50, Number 4 (2010), 727-752.
Poisson deformations of affine symplectic varieties, II
This article is a continuation of previous work, which has the same title. Let be an affine symplectic variety with a -action with positive weights, and let be its crepant resolution. Then induces a natural map of Kuranishi spaces for the Poisson deformations of and . In Part I, we proved that and are both nonsingular, and this map is a finite surjective map. In this article (Part II), we prove that it is a Galois covering. Markman already obtained a similar result in the compact case, which was a motivation for this article. As an application, we construct explicitly the universal Poisson deformation of the normalization of a nilpotent orbit closure in a complex simple Lie algebra when has a crepant resolution.
Kyoto J. Math., Volume 50, Number 4 (2010), 727-752.
First available in Project Euclid: 29 November 2010
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Namikawa, Yoshinori. Poisson deformations of affine symplectic varieties, II. Kyoto J. Math. 50 (2010), no. 4, 727--752. doi:10.1215/0023608X-2010-012. https://projecteuclid.org/euclid.kjm/1291041216