On small deformations of balanced manifolds

Abstract

We introduce a property of compact complex manifolds under which the existence of balanced metric is stable by small deformations of the complex structure. This property, which is weaker than the $\partial \overline{\partial }$-Lemma, is characterized in terms of the strongly Gauduchon cone and of the first $\partial \overline{\partial }$-degree measuring the difference of Aeppli and Bott-Chern cohomologies with respect to the Betti number $b_1$.

References in corpus (3)

• Autour de la cohomologie de Bott-Chern
• Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds
• Locally conformal Hermitian metrics on complex non-Kähler manifolds

Cited by in corpus (8)

• Lectures on the Strominger system
• On local stabilities of $p$-Kähler structures
• Deformations of Dolbeault cohomology classes
• Power series proofs for local stabilities of Kähler and balanced structures with mild $\partial \bar{\partial }$-lemma
• Deformed Aeppli cohomology: canonical deformations and jumping formulas
• On the Hermitian Geometry of $k$-Gauduchon Orthogonal Complex Structures
• Weak forms of $\ddb-$Lemma on compact complex manifolds
• On extension of closed complex (basic) differential forms: (basic) Hodge numbers and (transversely) $p$-Kähler structures