Poisson Cohomology of holomorphic toric Poisson manifolds. II

2019/11/07 by Hong, Wei · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1911.04331

Abstract

In this paper, we give a description of holomorphic multi-vector fields on smooth compact toric varieties, which generalizes Demazure's result of holomorphic vector fields on toric varieties. Based on the result, we compute the Poisson cohomology groups of holomorphic toric Poisson manifolds, i.e., toric varieties endowed with T-invariant holomorphic Poisson structures.

Cited by

• Atiyah constructions for Lie algebroid connections on fiber bundles

Related

• Toric Poisson Structures
• An approach to the tangential Poisson cohomology based on examples in duals of Lie algebras
• Holomorphic Poisson Cohomology
• Cohomology groups of homogeneous Poisson structures
• Computations of Nambu-Poisson cohomologies