# Modules of Square Integrable Holomorphic Germs

@article{Lempert2017ModulesOS, title={Modules of Square Integrable Holomorphic Germs}, author={L{\'a}szl{\'o} Lempert}, journal={arXiv: Complex Variables}, year={2017}, pages={311-333} }

This paper was inspired by Guan and Zhou’s recent proof of the socalled strong openness conjecture for plurisubharmonic functions. We give a proof shorter than theirs and extend the result to possibly singular Hermitian metrics on vector bundles.

## 30 Citations

A general extension theorem for cohomology classes on non reduced analytic subspaces

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- 2017

The main purpose of this paper is to generalize the celebrated L2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular…

On the extension of holomorphic sections from reduced unions of strata of divisors

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In this paper we study the problem of extension of holomorphic sections of line bundles/vector bundles from reduced unions of strata of divisors. An extension theorem of Ohsawa--Takegoshi type is…

Variation of Numerical Dimension of Singular Hermitian Line Bundles

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The purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from an observation for…

On the Multiplier Submodule Sheaves Associated to Singular Nakano Semi-positive Metrics

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- 2021

In this article, we establish the strong openness and stability property of multiplier submodule sheaves associated to singular Nakano semi-positive metrics on holomorphic vector bundles,…

Themes on Non-analytic Singularities of Plurisubharmonic Functions

- Mathematics
- 2015

We survey some results and questions on the singularity of psh functions with non-analytic singularities. Also we show that the Demailly approximation sequence of a psh function does not contain a…

Injectivity theorems with multiplier ideal sheaves for higher direct images under Kähler morphisms

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The purpose of this paper is to establish injectivity theorems for higher direct image sheaves of canonical bundles twisted by pseudo-effective line bundles and multiplier ideal sheaves. As…

AN OPTIMAL SUPPORT FUNCTION RELATED TO THE STRONG OPENNESS CONJECTURE

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- 2022

In the present article, we obtain an optimal support function of weighted L2 integrations on superlevel sets of psh weights, which implies the strong openness property of multiplier ideal sheaves.

On the Cohomology of Pseudoeffective Line Bundles

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The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact Kahler manifolds, and related properties of their multiplier ideal sheaves.…

Concavity of Minimal L2 Integrals Related to Multiplier Ideal Sheaves

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In this article, we present the concavity of the minimal $$L^2$$ L 2 integrals related to multiplier ideals sheaves on Stein manifolds. As applications, we obtain a necessary condition for the…

Extension of holomorphic functions and cohomology classes from non reduced analytic subvarieties

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The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity…

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