We provide further techniques to study the Dolbeault and Bott-Chern cohomologies of deformations of solvmanifolds by means of finite-dimensional complexes. By these techniques, we can compute the Dolbeault and Bott-Chern cohomologies of some complex solvmanifolds, and we also get explicit examples, showing in particular that either the $partialarpartial$-Lemma or the property that the Hodge and Fr"olicher spectral sequence degenerates at the first level are not closed under deformations.

Cohomologies of deformations of solvmanifolds and closedness of some properties / Angella, Daniele; Kasuya, Hisashi. - In: NORTH-WESTERN EUROPEAN JOURNAL OF MATHEMATICS. - ISSN 2496-5170. - ELETTRONICO. - 3:(2017), pp. 75-105.

Cohomologies of deformations of solvmanifolds and closedness of some properties

Angella, Daniele;Kasuya, Hisashi
2017

Abstract

We provide further techniques to study the Dolbeault and Bott-Chern cohomologies of deformations of solvmanifolds by means of finite-dimensional complexes. By these techniques, we can compute the Dolbeault and Bott-Chern cohomologies of some complex solvmanifolds, and we also get explicit examples, showing in particular that either the $partialarpartial$-Lemma or the property that the Hodge and Fr"olicher spectral sequence degenerates at the first level are not closed under deformations.
2017
3
75
105
Angella, Daniele; Kasuya, Hisashi
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1009011
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