scholarly journals Poisson cohomology of plane Poisson structures with isolated singularities revisited

2020 ◽  
Vol 61 (11) ◽  
pp. 111703
Author(s):  
Zihao Qi ◽  
Guodong Zhou
Keyword(s):  
Poisson Structures ◽  
Isolated Singularities ◽  
Poisson Cohomology

scholarly journals On a Non Logsymplectic Logarithmic Poisson Structure with Poisson Cohomology Isomorphic to the Associated Logarithmic Poisson Cohomology

2017 ◽  
Vol 9 (1) ◽  
pp. 109
Author(s):  
Joseph Dongho
Keyword(s):  
Poisson Structure ◽  
Poisson Structures ◽  
Cohomology Groups ◽  
Poisson Cohomology

The main purpose of this article is to show that there are non logsymplectic Poisson structures whose Poisson cohomology groups are isomorphic to corresponding logarithmic Poisson cohomology groups.

scholarly journals A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds

2017 ◽  
Vol 4 (1) ◽  
pp. 137-154 ◽  
Author(s):  
Yat Sun Poon ◽  
John Simanyi
Keyword(s):  
Spectral Sequence ◽  
Complex Structure ◽  
Adjoint Action ◽  
Poisson Structures ◽  
Dolbeault Cohomology ◽  
Poisson Cohomology ◽  
Abelian Complex Structure ◽  
Nijenhuis Bracket ◽  
Holomorphic Poisson Cohomology ◽  
Type Decomposition

Abstract A cohomology theory associated to a holomorphic Poisson structure is the hypercohomology of a bicomplex where one of the two operators is the classical მ̄-operator, while the other operator is the adjoint action of the Poisson bivector with respect to the Schouten-Nijenhuis bracket. The first page of the associated spectral sequence is the Dolbeault cohomology with coefficients in the sheaf of germs of holomorphic polyvector fields. In this note, the authors investigate the conditions for which this spectral sequence degenerates on the first page when the underlying complex manifolds are nilmanifolds with an abelian complex structure. For a particular class of holomorphic Poisson structures, this result leads to a Hodge-type decomposition of the holomorphic Poisson cohomology. We provide examples when the nilmanifolds are 2-step.

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