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arXiv · 1609.05637

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

Sheng Rao·Xueyuan Wan·Quanting Zhao
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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.

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Sheng Rao, Xueyuan Wan, Quanting Zhao. 2021-04-27. Power series proofs for local stabilities of Kähler and balanced structures with mild $\partial\bar\partial$-lemma. https://arxiv.org/abs/1609.05637

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