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arXiv · 1310.6083

Extensions of Poisson Structures on Singular Hypersurfaces

Aaron McMillan Fraenkel
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Abstract

Fix a codimension-1 affine Poisson variety $(X,π_X)$ in $\mathbb{C}^n$ with an isolated singularity at the origin. We characterize possible extensions of $π_X$ to $\mathbb{C}^n$ using the Koszul complex of the Jacobian ideal of $X$. In the particular case of a singular surface, we show that there always exists an extension of $π_X$ to $\mathbb{C}^n$.

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Aaron McMillan Fraenkel. 2013-12-18. Extensions of Poisson Structures on Singular Hypersurfaces. https://arxiv.org/abs/1310.6083

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