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Recent progress in the theory of functions of several complex variables and complex geometry

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Abstract

We give a survey on recent progress on converses of \(L^2\) existence theorem and \(L^2\) extension theorem which are two main parts in \(L^2\)-theory, and their applications in getting criteria of Griffiths positivity and characterizations of Nakano positivity of (singular) Hermitian metrics of holomorphic vector bundles, as well as the strong openness property and stability property of multiplier submodule sheaves associated to singular Nakano semipositive Hermitian metrics on holomorphic vector bundles.

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Funding

The author was partially supported by National Natural Science Foundation of China (grant No. 12288201) and by the National Key R&D Program of China (grant No. 2021YFA1003100).

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China

    Xiangyu Zhou

  2. Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, China

    Xiangyu Zhou

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  1. Xiangyu Zhou
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Correspondence to Xiangyu Zhou.

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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, 2024, Vol. 218, pp. 187–203 https://doi.org/10.4213/tmf10554.

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Zhou, X. Recent progress in the theory of functions of several complex variables and complex geometry. Theor Math Phys 218, 163–176 (2024). https://doi.org/10.1134/S0040577924010112

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  • DOI: https://doi.org/10.1134/S0040577924010112

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