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Poisson structures over a complete intersection with isolated singularities

Benoit Fresse
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Abstract

We study Poisson structures over singular varieties. In this purpose, we consider the Koszul complex associated to the equations of a complete intersection. This complex forms a differential graded algebra which is equivalent to the algebra of the variety. We show that a Poisson structure is equivalent to a sequence of multiderivations over the Koszul complex. If our variety has isolated singularities, then we can construct a sequence of multiderivations of reduced form.

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Benoit Fresse. 2002-02-14. Poisson structures over a complete intersection with isolated singularities. https://arxiv.org/abs/math/0202038

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