# 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}
}
• L. Lempert
• Published 1 April 2014
• Mathematics
• arXiv: Complex Variables
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.
A general extension theorem for cohomology classes on non reduced analytic subspaces
• Mathematics
• 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
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
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
• Mathematics
• 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
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
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
• Mathematics
• 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
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
• Mathematics
Peking Mathematical Journal
• 2022
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
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

## References

SHOWING 1-10 OF 34 REFERENCES
STRONG OPENNESS CONJECTURE FOR PLURISUBHARMONIC FUNCTIONS
• Mathematics
• 2013
In this article, we give a proof of the strong openness conjecture for plurisubharmonic functions posed by Demailly.
A maximum principle for hermitian (and other) metrics
We consider homomorphisms of hermitian holomorphic Hilbert bundles. Assuming the homomorphism decreases curvature, we prove that its pointwise norm is plurisubharmonic.
Bergman kernels and the pseudoeffectivity of relative canonical bundles
• Mathematics
• 2007
A criterion for the pseudoeffectivity of (twisted ) relative canonical bundles of surjective projective maps.
The openness conjecture for plurisubharmonic functions
We give a proof of the openness conjecture of Demailly and Ko llár.
Curvature of vector bundles associated to holomorphic fibrations
Let L be a (semi)-positive line bundle over a Kahler manifold, X, fibered over a complex manifold Y. Assuming the fibers are compact and nonsingular we prove that the hermitian vector bundle E over Y
On the Ohsawa-Takegoshi extension theorem
Motivated by a recent work by B.-Y. Chen we prove a new estimate for the @-operator, which easily implies the Ohsawa{Takegoshi extension theorem. We essentially only use the classical Hormander
Strong openness conjecture and related problems for plurisubharmonic functions
• Mathematics
• 2014
In this article, we solve the strong openness conjecture on the multiplier ideal sheaves for the plurisubharmonic functions posed by Demailly. We prove two conjectures about the growth of the volumes
A Sobolev mapping property of the Bergman kernel
• Mathematics
• 2000
Abstract. We prove that if D is a pseudoconvex domain with Lipschitz boundary having an exhaustion function $\rho$ such that $-(-\rho)^{\eta}$ is plurisubharmonic, then the Bergman projection maps