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

References in corpus (4)

• Optimal constant in an L^2 extension problem and a proof of a conjecture of Ohsawa
• Strong openness conjecture for plurisubharmonic functions
• Strong openness conjecture and related problems for plurisubharmonic functions
• Dynamic multiplier ideal sheaves and the construction of rational curves in Fano manifolds

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• A sharp effectiveness result of Demailly's strong openness conjecture
• Multiplier ideal sheaves, jumping numbers, and the restriction formula
• Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain V--fibrations over open Riemann surfaces
• Multiplier Submodule Sheaves and a problem of Lempert
• Equivalence of plurisubharmonic singularities and Siu-type metrics
• Extension of cohomology classes and holomorphic sections defined on subvarieties
• ACC for log canonical threshold polytopes
• Characterization of multiplier ideal sheaves with weights of Lelong number one
• Log canonical thresholds and Monge-Ampere masses
• 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
• Estimation of weighted $L^2$ norm related to Demailly's Strong Openness Conjecture
• Twisted version of Strong openness property in $L^p$
• Residue functions and Extension problems
• Effectiveness of strong openness property in $L^p$
• A Hilbert bundle approach to the sharp strong openness theorem and the Ohsawa-Takegoshi extension theorem
• A note on $\xi -$Bergman kernels
• A generalization of Nadel vanishing theorem
• Extension from lc centres and the extension theorem of Demailly but with estimates
• A support function of the weighted $L^2$ integrations on the superlevel sets of the weights
• 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