Multiplier ideal sheaves associated with weights of log canonical threshold one

Guan, Qian; Li, Zhenqian

doi:10.1016/j.aim.2016.07.012

Cited by 2 publications

(5 citation statements)

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“…Remark 5.18. As an immediate consequence of Corollary 5.17, we can obtain Theorem 1.2 in [22]. Remark A.2.…”

Section: Log Canonical Singularities Of Plurisubharmonic Functionsmentioning

confidence: 66%

“…In [22], we answered the above Question affirmatively in dimension two. Owing to the absence of desingularization theorem for plurisubharmonic functions, we cannot deal with the above question like the algebraic situation, and so it is reasonable to find another plurisubharmonic weight with mild singularities whose multiplier ideal cuts out the same subscheme as V(u).…”

Section: Introductionmentioning

confidence: 72%

“…Based on Theorem 1.19, in a subsequent paper [23], we are able to answer the Question posed in [22] for the three-dimensional case, by combining the Ohsawa-Takegoshi L 2 extension theorem proved in [47] with the restriction formula established in [27]. In particular, we can prove the following result in [23]:…”

Section: Introductionmentioning

confidence: 93%

“…Remark 5.20. We refer to [23] for an alternative argument of the case (b) by the so-called "inversion of adjunction" ([17], Theorem 2.5). Remark 5.21.…”

mentioning

confidence: 99%

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A note on multiplier ideal sheaves on complex spaces with singularities

2020

Preprint

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The goal of this note is to present some recent results of our research concerning multiplier ideal sheaves on complex spaces and singularities of plurisubharmonic functions. We firstly introduce multiplier ideal sheaves on complex spaces (not necessarily normal) via Ohsawa's extension measure, as a special case of which, it turns out to be the so-called Mather-Jacobian multiplier ideals in the algebro-geometric setting. As applications, we obtain a reasonable generalization of (algebraic) adjoint ideal sheaves to the analytic setting and establish some extension theorems on Kähler manifolds from singular hypersurfaces. Relying on our multiplier and adjoint ideals, we also give characterizations for several important classes of singularities of pairs associated to plurisubharmonic functions.Moreover, we also investigate the local structure of singularities of log canonical locus of plurisubharmonic functions. Especially, in the three-dimensional case, we show that for any plurisubharmonic function with log canonical singularities, its associated multiplier ideal subscheme is weakly normal, by which we give a complete classification of multiplier ideal subschemes with log canonical singularities.

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“…Remark 5.18. As an immediate consequence of Corollary 5.17, we can obtain Theorem 1.2 in [22]. Remark A.2.…”

Section: Log Canonical Singularities Of Plurisubharmonic Functionsmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 93%

“…Remark 5.20. We refer to [23] for an alternative argument of the case (b) by the so-called "inversion of adjunction" ([17], Theorem 2.5). Remark 5.21.…”

mentioning

confidence: 99%

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A note on multiplier ideal sheaves on complex spaces with singularities

2020

Preprint

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show abstract

“…Some elements of pluripotential theory that are used in the following are given by [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Proof Of Theorem 13mentioning

confidence: 99%

Semi-continuity properties of weighted log canonical thresholds of toric plurisubharmonic functions

Hong

2017

Comptes Rendus. Mathématique

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Multiplier ideal sheaves associated with weights of log canonical threshold one

Cited by 2 publications

References 5 publications

A note on multiplier ideal sheaves on complex spaces with singularities

A note on multiplier ideal sheaves on complex spaces with singularities

Semi-continuity properties of weighted log canonical thresholds of toric plurisubharmonic functions

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