Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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D. Angella - H. Kasuya

Bott-Chern cohomology of solvmanifolds

created by daniele on 22 Jun 2016
modified on 11 Jul 2017

[BibTeX]

Accepted Paper

Inserted: 22 jun 2016
Last Updated: 11 jul 2017

Journal: Ann. Global Anal. Geom.
Year: 2017
Doi: 10.1007/s10455-017-9560-6
Links: arXiv:1212.5708

Abstract:

We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott-Chern cohomology. We are especially aimed at studying the Bott-Chern cohomology of special classes of solvmanifolds, namely, complex parallelizable solvmanifolds and solvmanifolds of splitting type. More precisely, we can construct explicit finite-dimensional double complexes that allow to compute the Bott-Chern cohomology of compact quotients of complex Lie groups, respectively, of some Lie groups of the type $\mathbb{C}^n\ltimes_\varphi N$ where $N$ is nilpotent. As an application, we compute the Bott-Chern cohomology of the complex parallelizable Nakamura manifold and of the completely-solvable Nakamura manifold. In particular, the latter shows that the property of satisfying the $\partial\overline\partial$-Lemma is not strongly-closed under deformations of the complex structure.

Tags: SIR2014-AnHyC
, FIRB2012-DGGFT

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