Effectiveness of Demailly's strong openness conjecture and related problems

Abstract

In this article, stimulated by the effectiveness in Berndtsson's solution of the openness conjecture and continuing our solution of Demailly's strong openness conjecture, we discuss conditions to guarantee the effectiveness of the conjecture and establish such an effectiveness result. We explicitly point out a lower semicontinuity property of plurisubharmonic functions with a multiplier, which is implicitly contained in our paper arXiv:1401.7158. We also obtain optimal effectiveness of the conjectures of Demailly-Kollár and Jonsson-Mustată respectively.

31 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:1401.7158

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Cited by in corpus (27)

• Strong openness of multiplier ideal sheaves and optimal $L^2$ extension
• The closures of test configurations and algebraic singularity types
• A Nadel vanishing theorem for metrics with minimal singularities on big line bundles
• Extension with log-canonical measures and an improvement to the plt extension of Demailly--Hacon--Paun
• Multiplier ideal sheaves, jumping numbers, and the restriction formula
• A sharp effectiveness result of Demailly's strong openness conjecture
• Multiplier Submodule Sheaves and a problem of Lempert
• Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain V--fibrations over open Riemann surfaces
• Extension of cohomology classes and holomorphic sections defined on subvarieties
• ACC for log canonical threshold polytopes
• Equivalence of plurisubharmonic singularities and Siu-type metrics
• Characterization of multiplier ideal sheaves with weights of Lelong number one
• Concavity of minimal $L^2$ integrals related to multipler ideal sheaves
• Boundary asymptotics of the relative Bergman kernel metric for curves
• General concavity of minimal $L^2$ integrals related to multiplier ideal sheaves
• Log canonical thresholds and Monge-Ampere masses
• Twisted version of Strong openness property in $L^p$
• Estimation of weighted $L^2$ norm related to Demailly's Strong Openness Conjecture
• A generalization of Nadel vanishing theorem
• A support function of the weighted $L^2$ integrations on the superlevel sets of the weights
• A note on $\xi -$Bergman kernels
• A global approximation result by Al Taylor and the strong openness conjecture in C^n
• Lelong numbers, complex singularity exponents, and Siu's semicontinuity theorem
• A Hilbert bundle approach to the sharp strong openness theorem and the Ohsawa-Takegoshi extension theorem
• Residue functions and Extension problems
• Extension from lc centres and the extension theorem of Demailly but with estimates
• Effectiveness of strong openness property in $L^p$