POWER SERIES PROOFS FOR LOCAL STABILITIES OF KÄHLER AND BALANCED STRUCTURES WITH MILD $\partial \overline {\partial }$ -LEMMA

IF 0.8 2区 数学 Q2 MATHEMATICS Nagoya Mathematical Journal Pub Date : 2021-06-08 DOI:10.1017/nmj.2021.4
S. Rao, Xueyuan Wan, Quanting Zhao
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引用次数: 10

Abstract

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 $\partial \overline {\partial }$ -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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具有MILD$\partial\overline{\partial}$-LEMA的KöHLER和平衡结构局部稳定性的幂级数证明
利用第一和第三作者最近介绍的从复流形上的纯型复微分形式空间到该流形的小可微变形上的相应空间的自然映射,给出了Kähler结构的Kodaira-Spencer局部稳定性定理的幂级数证明。我们还得到了两个新的局部稳定性定理,一个是关于n维平衡流形上的平衡结构的,用幂级数法得到了$(n-1,n)$温和的$\partial \overline {\partial }$ -引理,另一个是关于p-Kähler结构的,用$(p,p)$ - bot - chern数的变形不变性。
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来源期刊
CiteScore
1.60
自引率
0.00%
发文量
31
审稿时长
6 months
期刊介绍: The Nagoya Mathematical Journal is published quarterly. Since its formation in 1950 by a group led by Tadashi Nakayama, the journal has endeavoured to publish original research papers of the highest quality and of general interest, covering a broad range of pure mathematics. The journal is owned by Foundation Nagoya Mathematical Journal, which uses the proceeds from the journal to support mathematics worldwide.
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