On the $\partial \overline{\partial }$-Lemma and Bott-Chern cohomology

Abstract

On a compact complex manifold $X$, we prove a Frölicher-type inequality for Bott-Chern cohomology and we show that the equality holds if and only if $X$ satisfies the $\partial \overline{\partial }$-Lemma.

Cited by in corpus (24)

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• On Bott-Chern cohomology of compact complex surfaces
• On small deformations of balanced manifolds
• On local stabilities of $p$-Kähler structures
• On the Structure of Double Complexes
• Dolbeault and Bott-Chern formalities: deformations and $\partial \overline{\partial }$-lemma
• A Frölicher-type inequality for generalized complex manifolds
• On the deformed Bott-Chern cohomology
• On the cohomology of almost complex and symplectic manifolds and proper surjective maps
• Dolbeault cohomology of compact complex manifolds with an action of a complex Lie group
• Symplectic cohomologies and deformations
• On Bott-Chern and Aeppli cohomologies of almost complex manifolds and related spaces of harmonic forms
• Localization of Bott-Chern classes and Hermitian residues
• On non-Kähler degrees of complex manifolds
• Quaternionic Bott-Chern cohomology and existence of HKT metrics
• The $\partial \bar{\partial }$-lemma under surjective maps
• Geometric formalities along the Chern-Ricci flow
• Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds
• On extension of closed complex (basic) differential forms: (basic) Hodge numbers and (transversely) $p$-Kähler structures
• Stability of holomorphically-parallelizable manifolds
• Some computations on trivial canonical-bundle solvmanifolds