On Bott-Chern cohomology of compact complex surfaces

Abstract

We study Bott-Chern cohomology on compact complex non-Kähler surfaces. In particular, we compute such a cohomology for compact complex surfaces in class $\text{VII}$ and for compact complex surfaces diffeomorphic to solvmanifolds.

References in corpus (1)

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

Cited by in corpus (13)

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• Locally conformal Hermitian metrics on complex non-Kähler manifolds
• Compact Complex Manifolds with Small Gauduchon Cone
• On the cohomology of almost complex and symplectic manifolds and proper surjective maps
• On the deformed Bott-Chern cohomology
• Localization of Bott-Chern classes and Hermitian residues
• On Bott-Chern and Aeppli cohomologies of almost complex manifolds and related spaces of harmonic forms
• On non-Kähler degrees of complex manifolds
• Quaternionic Bott-Chern cohomology and existence of HKT metrics
• Geometric formalities along the Chern-Ricci flow
• Bott-Chern Laplacian on almost Hermitian manifolds
• On canonical metrics of complex surfaces with split tangent and related geometric PDEs
• Hermitian ranks of compact complex manifolds