Power series proofs for local stabilities of Kähler and balanced structures with mild $\partial \bar{\partial }$-lemma

Abstract

By use of a natural map introduced recently by the first and third authors from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the small differentiable deformation of this manifold, we will give a power series proof for Kodaira-Spencer's local stability theorem of Kähler structures. We also obtain two new local stability theorems, one of balanced structures on an $n$-dimensional balanced manifold with the $(n-1,n)$-th mild $\partial \bar{\partial }$-lemma by power series method and the other one on $p$-Kähler structures with the deformation invariance of $(p,p)$-Bott-Chern numbers.

Final to appear in Nagoya Math. J.. All comments and remarks are welcome

References in corpus (3)

• Geometry of nilmanifolds with left-invariant complex structure and deformations in the large
• On Deformations of Generalized Complex Structures: the Generalized Calabi-Yau Case
• Extension formulas and deformation invariance of Hodge numbers

Cited by in corpus (1)

• Solving equations with Hodge theory