Poisson structures over a complete intersection with isolated singularities

2002/02/14 by Benoit Fresse
Mathematics · #math.RA #math.AC #math.SG #msc:17B63 #msc:53D17 #msc:14M10 #msc:14B05 #msc:13N05

paper · pdf

published as C. R. Acad. Sci. Paris Ser. I Math. 335 (2002), pp. 5-10 · Projet de note aux C.R.Acad.Sci.Paris

arxiv created 2002/02/14 · arxiv updated 2009/11/30

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.

Related

• Extensions of Poisson Structures on Singular Hypersurfaces
• Poisson structure on bi-graded spaces and Koszul duality, I. The classical case
• Shifted Poisson structures and moduli spaces of complexes
• Batalin-Vilkovisky algebra structure on Poisson manifolds with diagonalizable modular symmetry
• Poisson geometry of the moduli of local systems on smooth varieties