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The \(\partial \bar \partial \)-Lemma under Surjective Maps

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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.

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Acknowledgements

The author warmly thanks Sheng Rao, Song Yang, Xiang-Dong Yang and Jonas Stelzig [17] for useful discussions.

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Authors and Affiliations

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

    Lingxu Meng  (孟令旭)

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  1. Lingxu Meng  (孟令旭)
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Correspondence to Lingxu Meng  (孟令旭).

Additional information

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).

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Meng, L. The \(\partial \bar \partial \)-Lemma under Surjective Maps. Acta Math Sci 42, 865–875 (2022). https://doi.org/10.1007/s10473-022-0303-9

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  • DOI: https://doi.org/10.1007/s10473-022-0303-9

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