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

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Title: Recent progress in the theory of functions of several complex variables and complex geometry.
Authors: Zhou, Xiangyu1,2 (AUTHOR) xyzhou@math.ac.cn
Source: Theoretical & Mathematical Physics. Jan2024, Vol. 218 Issue 1, p163-176. 14p.
Subjects: Functions of several complex variables, Mathematical complex analysis, Complex variables, Sheaf theory, Vector bundles, Geometry, Complex geometry
Abstract: We give a survey on recent progress on converses of existence theorem and extension theorem which are two main parts in -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. [ABSTRACT FROM AUTHOR]
Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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PubType: Academic Journal
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  Data: Recent progress in the theory of functions of several complex variables and complex geometry.
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  Data: <searchLink fieldCode="DE" term="%22Functions+of+several+complex+variables%22">Functions of several complex variables</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+complex+analysis%22">Mathematical complex analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Complex+variables%22">Complex variables</searchLink><br /><searchLink fieldCode="DE" term="%22Sheaf+theory%22">Sheaf theory</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+bundles%22">Vector bundles</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Complex+geometry%22">Complex geometry</searchLink>
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  Data: We give a survey on recent progress on converses of existence theorem and extension theorem which are two main parts in -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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1134/S0040577924010112
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 163
    Subjects:
      – SubjectFull: Functions of several complex variables
        Type: general
      – SubjectFull: Mathematical complex analysis
        Type: general
      – SubjectFull: Complex variables
        Type: general
      – SubjectFull: Sheaf theory
        Type: general
      – SubjectFull: Vector bundles
        Type: general
      – SubjectFull: Geometry
        Type: general
      – SubjectFull: Complex geometry
        Type: general
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      – TitleFull: Recent progress in the theory of functions of several complex variables and complex geometry.
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              M: 01
              Text: Jan2024
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              Y: 2024
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