Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (3): 865-875.doi: 10.1007/s10473-022-0303-9

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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,
  • 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).

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

CLC Number: 

  • 32Q99