The weighted log canonical threshold

By Phạm Hoàng Hiệp. 2014

86 citations recorded by the source corpus.

In this note, we show how to apply the original $L^2$-extension theorem of Ohsawa and Takegoshi to the standard basis of a multiplier ideal sheaf associated with a plurisubharmonic function. In this way, we are able to reprove the strong openness conjecture and to obtain an effective version of the semicontinuity theorem for weighted log canonical thresholds.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b474155511de1f2b4fdfe172dc7e8fd9cdb057a4

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

A general extension theorem for cohomology classes on non reduced analytic subspaces (2017, background): “ve, we infer that property (d) holds. Finally we check the last conclusion of property (c) by proving the following lemma, which can be obtained from the strong openness theorem (see [GZ15], [Lem14], [Hie14]) and property (e). Lemma3.3. For a quasi-psh function ϕ, we have I(he−ϕ) = I(hεe−ϕ). In part”
Modules of Square Integrable Holomorphic Germs (2014, result): “harmonic, then I(u) = I(ηu) with some η∈ (1,∞). After partial results by Favre-Jonsson and Berndtsson, Guan and Zhou recently posted a proof of the conjecture, see [B3,FJ,GZ2-4]. A related posting is [Hi]. Our main purpose with this paper is to produce a proof, as we hope more transparent than Guan-”
The openness conjecture and complex Brunn-Minkowski inequalities (2014, methodology): “The strong openness conjecture was proved by Guan-Zhou in [13], see also Hiep [16] and Lempert [19].”
A sharp effectiveness result of Demailly's strong openness conjecture (2017, background): “Recently, SOC was proved in [15] (see also [23, 18]).”
An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (2013, unknown): “on of algebraic singularities. Remark 4.3. Three months after we ﬁnish writing our preprint, Guan and Zhou proved the strong openness conjecture in [GZ13]. Further another proof was given by Hiˆep in [Hie14] and by Lempert in [Lem14]. Although their celebrated result and Cao’s theorem lead to Coroll”