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

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-02-01 DOI:10.1134/s0040577924010112

Xiangyu Zhou

引用次数: 0

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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若干复变函数和复几何学理论的最新进展

摘要我们对（L^2\）理论的两个主要部分--（L^2\）存在定理和（L^2\）扩展定理--的会话的最新进展，以及它们在获得格里菲斯实在性标准和全形向量束（奇异）赫米特度量的中野实在性特征方面的应用进行了综述、以及与全形向量束上奇异中野半正赫米提度量相关的乘子子模剪的强开放性性质和稳定性性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.