Cohomologies of deformations of solvmanifolds and closedness of some properties

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 $\partial \overline{\partial }$-Lemma or the property that the Hodge and Frölicher spectral sequence degenerates at the first level are not closed under deformations.

Cited by in corpus (7)

• Non-Kähler Calabi-Yau manifolds
• The Double Complex of a Blow-up
• Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
• On small deformations of balanced manifolds
• Six dimensional solvmanifolds with holomorphically trivial canonical bundle
• Complex symplectic structures and the $\partial \bar{\partial }$-lemma
• The $\partial \bar{\partial }$-lemma under surjective maps