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Complex Manifolds

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Holomorphic Poisson Cohomology

Zhuo Chen / Daniele Grandini
  • Corresponding author
  • Department of Mathematics, Virginia Commonwealth University, Richmond, VA 23284, U.S.A
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Yat-Sun Poon
  • Corresponding author
  • Department of Mathematics, University of California at Riverside, Riverside, CA 92521, U.S.A
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-07-13 | DOI: https://doi.org/10.1515/coma-2015-0005

Abstract

Holomorphic Poisson structures arise naturally in the realm of generalized geometry. A holomorphic Poisson structure induces a deformation of the complex structure in a generalized sense, whose cohomology is obtained by twisting the Dolbeault @-operator by the holomorphic Poisson bivector field. Therefore, the cohomology space naturally appears as the limit of a spectral sequence of a double complex. The first sheet of this spectral sequence is simply the Dolbeault cohomology with coefficients in the exterior algebra of the holomorphic tangent bundle. We identify various necessary conditions on compact complex manifolds on which this spectral sequence degenerates on the level of the second sheet. The manifolds to our concern include all compact complex surfaces, Kähler manifolds, and nilmanifolds with abelian complex structures or parallelizable complex structures.

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About the article

Received: 2015-01-10

Accepted: 2015-05-27

Published Online: 2015-07-13


Citation Information: Complex Manifolds, Volume 2, Issue 1, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2015-0005.

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© 2015 Zhuo Chen et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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