Kyoto Journal of Mathematics

Poisson deformations of affine symplectic varieties, II

Yoshinori Namikawa

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This article is a continuation of previous work, which has the same title. Let Y be an affine symplectic variety with a C-action with positive weights, and let π:XY be its crepant resolution. Then π induces a natural map PDef(X)PDef(Y) of Kuranishi spaces for the Poisson deformations of X and Y. In Part I, we proved that PDef(X) and PDef(Y) 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 O˜ of a nilpotent orbit closure O˜ in a complex simple Lie algebra when O˜ has a crepant resolution.

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Kyoto J. Math., Volume 50, Number 4 (2010), 727-752.

First available in Project Euclid: 29 November 2010

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Zentralblatt MATH identifier

Primary: 14J 14E 32G
Secondary: 14B 32J


Namikawa, Yoshinori. Poisson deformations of affine symplectic varieties, II. Kyoto J. Math. 50 (2010), no. 4, 727--752. doi:10.1215/0023608X-2010-012.

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