Poisson Cohomology of holomorphic toric Poisson manifolds. I

Abstract

A holomorphic toric Poisson manifold is a nonsingular toric variety equipped with a holomorphic Poisson structure, which is invariant under the torus action. In this paper, we computed the Poisson cohomology groups for all holomorphic toric Poisson structures on $C{P}^n$, with the stand Poisson structure on $C{P}^n$ as a special case. We also computed the algebraic and the formal Poisson cohomology groups of holomorphic toric Poisson structures on $C^n$.

References in corpus (5)

• Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
• Poisson modules and generalized geometry
• Cyclicity of Lusztig's stratification of Grassmannians and Poisson geometry
• A Hodge-Type Decomposition of Holomorphic Poisson Cohomology on Nilmanifolds
• Deformations of compact holomorphic Poisson manifolds and algebraic Poisson schemes

Cited by in corpus (5)

• Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds
• Holomorphic polyvector fields on toric varieties
• Complete and vertical lifts of Poisson vector fields and infinitesimal deformations of Poisson tensor
• Frobenius Structures and Generalized Deformation of Kodaira Manifolds
• Holomorphic Koszul-Brylinski homology via Dolbeault cohomology