Algebraic Structure of Holomorphic Poisson Cohomology on Nilmanifolds

IF 0.5 Q3 MATHEMATICS Complex Manifolds Pub Date : 2018-09-11 DOI:10.1515/coma-2019-0004

Y. Poon, John Simanyi

引用次数: 3

Abstract

Abstract It is proved that on nilmanifolds with abelian complex structure, there exists a canonically constructed non-trivial holomorphic Poisson structure.We identify the necessary and sufficient condition for its associated cohomology to be isomorphic to the cohomology associated to trivial (zero) holomorphic Poisson structure. We also identify a sufficient condition for this isomorphism to be at the level of Gerstenhaber algebras.

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零流形上全纯Poisson同调的代数结构

摘要证明了在具有阿贝尔复结构的幂零流形上，存在一个经典构造的非平凡全纯泊松结构。我们确定了它的相关上同调同构于与平凡（零）全纯泊松结构相关的上同调的充要条件。我们还确定了这个同构在Gerstenhaber代数水平上的一个充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.

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