A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds

• Autorzy: Yat Sun Poon , John Simanyi
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Holomorphic Poisson; Cohomology; Hodge theory; Nilmanifolds

Kategorie tematyczne

• 18G40: Spectral sequences, hypercohomology
• 53D18: Generalized geometries (\`a la Hitchin)
• 53D17: Poisson manifolds; Poisson groupoids and algebroids
• 14D07: Variation of Hodge structures
• 32G20: Period matrices, variation of Hodge structure; degenerations

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2017
• Tom: 4
• Numer: 1
• Strony: 137-154

Daty

wydano

2017-02-23

otrzymano

2017-06-16

zaakceptowano

2017-07-12

online

2017-08-04

Twórcy

autor

Yat Sun Poon

• , CA 92521,

autor

John Simanyi

• , CA 92521,

Identyfikatory

DOI

10.1515/coma-2017-0009