Symplectic singularities from the Poisson point of view

D. Kaledin

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arXiv · math/0310186

Symplectic singularities from the Poisson point of view

D. Kaledin

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Abstract

We consider symplectic singularities in the sense of A. Beauville as examples of Poisson schemes. Using Poisson methods, we prove that a symplectic singularity admits a finite stratification with smooth symplectic strata. We also prove that in the formal neighborhood of a closed point in some stratum, the singularity is a product of the stratum and a transversal slice. The transversal slice is also a symplectic singularity, and the product decomposition is compatible with natural Poisson structures. Moreover, we prove that the transversal slice admits a $C^*$-action dilating the symplectic form.

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BibTeX RIS

D. Kaledin. 2006-03-09. Symplectic singularities from the Poisson point of view. https://arxiv.org/abs/math/0310186

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