Holomorphic Poisson Cohomology

• Autorzy: Zhuo Chen , Daniele Grandini , Yat-Sun Poon
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2015
• Tom: 2
• Numer: 1

Daty

otrzymano

2015-01-10

zaakceptowano

2015-05-27

online

2015-07-13

Twórcy

autor

Zhuo Chen

• Department of Mathematical Sciences, Tsinghua University, Beijing, P.R.C.

autor

Daniele Grandini

• Department of Mathematics, Virginia Commonwealth University, Richmond, VA
  23284, U.S.A

autor

Yat-Sun Poon

• Department of Mathematics, University of California at Riverside, Riverside, CA 92521, U.S.A

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Identyfikatory

DOI

10.1515/coma-2015-0005