Poisson structures over a complete intersection with isolated singularities

Details Poisson structures over a complete intersection with isolated singularities Poisson structures over a complete intersection with isolated singularities

2002-02-05

arxiv.org/abs/math/0202038v2

C. R. Acad. Sci. Paris Ser. I Math. 335 (2002), pp. 5-10

Mathematics

Rings and Algebras

Projet de note aux C.R.Acad.Sci.Paris

Scientific paper

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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