A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds

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 o...

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Autores principales:	Poon Yat Sun, Simanyi John
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2017
Materias:	holomorphic poisson cohomology hodge theory nilmanifolds 53d18 53d17 32g20 18g40 14d07 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/fd70e3e315f543cebff44d90f4a8db35
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id	oai:doaj.org-article:fd70e3e315f543cebff44d90f4a8db35
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spelling	oai:doaj.org-article:fd70e3e315f543cebff44d90f4a8db352021-12-02T16:36:59ZA Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds2300-744310.1515/coma-2017-0009https://doaj.org/article/fd70e3e315f543cebff44d90f4a8db352017-02-01T00:00:00Zhttps://doi.org/10.1515/coma-2017-0009https://doaj.org/toc/2300-7443A 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.Poon Yat SunSimanyi JohnDe Gruyterarticleholomorphic poissoncohomologyhodge theorynilmanifolds53d1853d1732g2018g4014d07MathematicsQA1-939ENComplex Manifolds, Vol 4, Iss 1, Pp 137-154 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	holomorphic poisson cohomology hodge theory nilmanifolds 53d18 53d17 32g20 18g40 14d07 Mathematics QA1-939
spellingShingle	holomorphic poisson cohomology hodge theory nilmanifolds 53d18 53d17 32g20 18g40 14d07 Mathematics QA1-939 Poon Yat Sun Simanyi John A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds
description	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.
format	article
author	Poon Yat Sun Simanyi John
author_facet	Poon Yat Sun Simanyi John
author_sort	Poon Yat Sun
title	A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds
title_short	A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds
title_full	A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds
title_fullStr	A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds
title_full_unstemmed	A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds
title_sort	hodge-type decomposition of holomorphic poisson cohomology on nilmanifolds
publisher	De Gruyter
publishDate	2017
url	https://doaj.org/article/fd70e3e315f543cebff44d90f4a8db35
work_keys_str_mv	AT poonyatsun ahodgetypedecompositionofholomorphicpoissoncohomologyonnilmanifolds AT simanyijohn ahodgetypedecompositionofholomorphicpoissoncohomologyonnilmanifolds AT poonyatsun hodgetypedecompositionofholomorphicpoissoncohomologyonnilmanifolds AT simanyijohn hodgetypedecompositionofholomorphicpoissoncohomologyonnilmanifolds
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A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds

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