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

• 论文 • 上一篇    下一篇

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

孟令旭   

  1. Department of Mathematics, North University of China, Taiyuan, 030051, China
  • 收稿日期:2020-06-15 修回日期:2021-04-14 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   

  1. Department of Mathematics, North University of China, Taiyuan, 030051, China
  • Received:2020-06-15 Revised:2021-04-14 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: 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