Dolbeault and Bott-Chern formalities: deformations and $\partial \overline{\partial }$-lemma

Abstract

It is proved that the properties of being Dolbeault formal and geometrically-Bott-Chern-formal are not closed under holomorphic deformations of the complex structure. Further, we construct a compact complex manifold which satisfies the $\partial \overline{\partial }$-lemma but admits a non vanishing Aeppli-Bott-Chern-Massey product.

References in corpus (9)

• On the $\partial \overline{\partial }$-Lemma and Bott-Chern cohomology
• The cohomologies of the Iwasawa manifold and of its small deformations
• On products of harmonic forms
• The Double Complex of a Blow-up
• Bott-Chern cohomology of solvmanifolds
• On Bott-Chern cohomology and formality
• Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
• On the Structure of Double Complexes
• Cohomologies of certain orbifolds

Cited by in corpus (2)

• Pluripotential Homotopy Theory
• Blowing up Chern-Ricci flat balanced metrics