Pseudo-effective line bundles over holomorphically convex manifolds

Meng, Xiankui; Zhou, Xiangyu

doi:10.1090/jag/714

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新近进展1

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2023

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Cited by 9 publications

(1 citation statement)

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“…利用乘子理想层的强开性, 孟宪奎和作者 [42] 在不需要 Kähler 流形假定下建立了 Nadel 消没定理; 还获得了取值乘子理想层的消没定理、有限性定理和满性定理, 推广了 Ohsawa 和 Peternell 关于光滑半正度量的相应定理 (参见文献 [43][44][45][46][47]).…”

Section: 新近进展unclassified

A brief introduction of several complex variables

Xiangyu¹

2019

Sci. Sin.-Math.

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庄圻泰先生与杨乐先生在为《中国大百科全书》数学卷撰写 "复变函数论" 条目时, 写道: "复变函数理论从一个变数推广到多个变数是十分自然的想法, 总称为复分析." 2 多复变是什么多复变函数论是 "数学中研究多个复变量的全纯函数的性质和结构的分支学科" (钟家庆,《中国大百科全书》数学卷). 用范畴 (category) 的语言来说, 多复变是研究复解析范畴的学问. 这里, 范畴的对象 (objects) 是复流形 (乃至复空间), 态射 (morphisms) 是复流形 (乃至复空间) 之间的复解析映照.

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Section: 新近进展unclassified

A brief introduction of several complex variables

Xiangyu¹

2019

Sci. Sin.-Math.

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On the Restriction Formula

Meng,

Zhou

2023

J Geom Anal

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Extension of cohomology classes and holomorphic sections defined on subvarieties

Zhou

Zhu

2021

J. Algebraic Geom.

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In this paper, we obtain two extension theorems for cohomology classes and holomorphic sections defined on analytic subvarieties, which are defined as the supports of the quotient sheaves of multiplier ideal sheaves of quasi-plurisubharmonic functions with arbitrary singularities. The first result gives a positive answer to a question posed by Cao-Demailly-Matsumura and unifies a few well-known injectivity theorems. The second result generalizes and optimizes a general L 2 L^2 extension theorem obtained by Demailly.

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Pseudo-effective line bundles over holomorphically convex manifolds

Abstract: In the present paper, we consider the pseudo-effective line bundles over holomorphically convex manifolds and obtain some results related to the vanishing, finiteness, and surjectivity of analytic cohomology groups with multiplier ideal sheaves.

Cited by 9 publications

References 41 publications

A brief introduction of several complex variables

A brief introduction of several complex variables

On the Restriction Formula

Extension of cohomology classes and holomorphic sections defined on subvarieties

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