Displaying similar documents to “Holomorphic Poisson Cohomology”

A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds

Yat Sun Poon, John Simanyi (2017)

Complex Manifolds

Similarity:

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...

Nonclassical descriptions of analytic cohomology

Bailey, Toby N., Eastwood, Michael G., Gindikin, Simon G.

Similarity:

Summary: There are two classical languages for analytic cohomology: Dolbeault and Čech. In some applications, however (for example, in describing the Penrose transform and certain representations), it is convenient to use some nontraditional languages. In [, and , J. Geom. Phys. 17, 231-244 (1995; Zbl 0861.22009)] was developed a language that allows one to render analytic cohomology in a purely holomorphic fashion.In this article we indicate a more general construction, which includes...

Remarks on the Lichnerowicz-Poisson cohomology

Izu Vaisman (1990)

Annales de l'institut Fourier

Similarity:

The paper begins with some general remarks which include the Mayer-Vietoris exact sequence, a covariant version of the Lichnerowicz-Poisson cohomology, and the definition of an associated Serre-Hochshild spectral sequence. Then we consider the regular case, and we discuss the Poisson cohomology by using a natural bigrading of the Lichnerowicz cochain complex. Furthermore, if the symplectic foliation of the Poisson manifold is either transversally Riemannian or transversally symplectic,...