On the deformed Bott-Chern cohomology

Abstract

Given a compact complex manifold $X$ and a integrable Beltrami differential $\varphi \in A^{0,1}(X,T_X^{1,0})$, we introduce a double complex structure on $A^{\bullet ,\bullet }(X)$ naturally determined by $\varphi$ and study its Bott-Chern cohomology. In particular, we establish a deformation theory for Bott-Chern cohomology and use it to compute the deformed Bott-Chern cohomology for the Iwasawa manifold and the holomorphically parallelizable Nakamura manifold. The $\partial {\bar{\partial }}_{\varphi }$-lemma is studied and we show a compact complex manifold satisfying $\partial {\bar{\partial }}_{\varphi }$-lemma is formal.

23 pages

References in corpus (5)

• Autour de la cohomologie de Bott-Chern
• The Double Complex of a Blow-up
• Deformations of Dolbeault cohomology classes
• Deformations of Dolbeault cohomology classes for Lie algebra with complex structures
• The heredity and bimeromorphic invariance of the $\partial \overline{\partial }$-lemma property

Cited by in corpus (3)

• Deformations of Dolbeault cohomology classes
• Deformations of Dolbeault cohomology classes for Lie algebra with complex structures
• On extension of closed complex (basic) differential forms: (basic) Hodge numbers and (transversely) $p$-Kähler structures