THE $\partial\bar{\partial}$-LEMMA UNDER SURJECTIVE MAPS

doi:10.1007/s10473-022-0303-9

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 865-875.doi: 10.1007/s10473-022-0303-9

THE $\partial\bar{\partial}$-LEMMA UNDER SURJECTIVE MAPS

孟令旭

Department of Mathematics, North University of China, Taiyuan, 030051, China

收稿日期:2020-06-15 修回日期:2021-04-14 出版日期:2022-06-26 发布日期:2022-06-24
通讯作者: Lingxu MENG,E-mail:menglingxu@nuc.edu.cn E-mail:menglingxu@nuc.edu.cn
基金资助:
The author is supported by the National Natural Science Foundation of China (12001500, 12071444), the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2020L0290) and the Natural Science Foundation of Shanxi Province of China (201901D111141).

THE $\partial\bar{\partial}$-LEMMA UNDER SURJECTIVE MAPS

Lingxu MENG

Department of Mathematics, North University of China, Taiyuan, 030051, China

Received:2020-06-15 Revised:2021-04-14 Online:2022-06-26 Published:2022-06-24
Contact: Lingxu MENG,E-mail:menglingxu@nuc.edu.cn E-mail:menglingxu@nuc.edu.cn
Supported by:
The author is supported by the National Natural Science Foundation of China (12001500, 12071444), the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2020L0290) and the Natural Science Foundation of Shanxi Province of China (201901D111141).

摘要/Abstract

摘要： We consider the $\partial\bar{\partial}$-lemma for complex manifolds under surjective holomorphic maps. Furthermore, using Deligne-Griffiths-Morgan-Sullivan's theorem, we prove that a product compact complex manifold satisfies the $\partial\bar{\partial}$-lemma if and only if all of its components do as well.

关键词: $\partial\bar{\partial}$-lemma, surjective holomorphic map, product complex manifold, fiber bundle, E₁-isomorphism

Abstract: We consider the $\partial\bar{\partial}$-lemma for complex manifolds under surjective holomorphic maps. Furthermore, using Deligne-Griffiths-Morgan-Sullivan's theorem, we prove that a product compact complex manifold satisfies the $\partial\bar{\partial}$-lemma if and only if all of its components do as well.

Key words: $\partial\bar{\partial}$-lemma, surjective holomorphic map, product complex manifold, fiber bundle, E₁-isomorphism

中图分类号:

32Q99

孟令旭. THE $\partial\bar{\partial}$-LEMMA UNDER SURJECTIVE MAPS[J]. 数学物理学报, 2022, 42(3): 865-875.

Lingxu MENG. THE $\partial\bar{\partial}$-LEMMA UNDER SURJECTIVE MAPS[J]. Acta mathematica scientia,Series A, 2022, 42(3): 865-875.

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THE $\partial\bar{\partial}$-LEMMA UNDER SURJECTIVE MAPS

THE $\partial\bar{\partial}$-LEMMA UNDER SURJECTIVE MAPS

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