Poisson (co)homology and isolated singularities

Abstract

To each polynomial $\v\in\F[x,y,z]$ is associated a Poisson structure on $\F^3$, a surface and a Poisson structure on this surface. When $\v$ is weight homogeneous with an isolated singularity, we determine the Poisson cohomology and homology of the two Poisson varieties obtained.

27 pages

Cited by in corpus (26)

• Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
• Twisted Poincare duality for some quadratic Poisson algebras
• On the Heisenberg invariance and the Elliptic Poisson tensors
• Poisson brackets and Poisson spectra in polynomial algebras
• The Zariski cancellation problem for Poisson algebras
• Holomorphic Koszul-Brylinski Homology
• Poisson structures and star products on quasimodular forms
• The Poisson cohomology of ${\mathfrak{sl}}_2^{\ast }(\mathbb{R})$
• Associative and Lie deformations of Poisson algebras
• Hochschild Homology and Cohomology of Klein Surfaces
• Twisted Poincaré duality between Poisson homology and Poisson cohomology
• Extensions of Poisson Structures on Singular Hypersurfaces
• Poisson structures on associated with rigid Lie algebras
• Reversible skew Laurent polynomial rings and deformations of Poisson automorphisms
• Calabi-Yau algebras viewed as deformations of Poisson algebras
• On Nash resolution of (singular) Lie algebroids
• On Embedding Singular Poisson Spaces
• Integer solutions of integral inequalities and H-invariant Jacobian Poisson structures
• Non-associative algebras associated to Poisson algebras
• Universal cocycles and the graph complex action on homogeneous Poisson brackets by diffeomorphisms
• On the Hochschild homology of elliptic Sklyanin algebras
• Poisson (co)homology of truncated polynomial algebras in two variables
• Cohomologie De Hochschild Des Surfaces De Klein
• Zeroth Poisson homology, foliated cohomology and perfect Poisson manifolds
• Deformations of Poisson algebras
• Formal deformations of Poisson structures in low dimensions