Extension formulas and deformation invariance of Hodge numbers

Abstract

We introduce a canonical isomorphism from the space of pure-type complex differential forms on a compact complex manifold to the one on its infinitesimal deformations. By use of this map, we generalize an extension formula in a recent work of K. Liu, X. Yang and the second author. As a direct corollary of the extension formulas, we prove several deformation invariance theorems for Hodge numbers on some certain classes of complex manifolds, without use of Frölicher inequality or the topological invariance of Betti numbers.

References in corpus (4)

• Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
• On Deformations of Generalized Complex Structures: the Generalized Calabi-Yau Case
• Holomorphic Deformations of Balanced Calabi-Yau $\partial \bar{\partial }$-Manifolds
• New proofs of the Torelli theorems for Riemann surfaces

Cited by in corpus (10)

• On local stabilities of $p$-Kähler structures
• Deformations of Dolbeault cohomology classes
• Deformations of Dolbeault cohomology classes for Lie algebra with complex structures
• Power series proofs for local stabilities of Kähler and balanced structures with mild $\partial \bar{\partial }$-lemma
• Several special complex structures and their deformation properties
• Deformed Aeppli cohomology: canonical deformations and jumping formulas
• A logarithmic $\bar{\partial }$-equation on a compact Kähler manifold associated to a smooth divisor
• 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
• Extension formulae on almost complex manifolds