A log Canonical Threshold Test

We give a restriction formula on jumping numbers which is a reformulation of Demailly–Ein–Lazarsfeld’s important restriction formula for multiplier ideal sheaves and a generalization of Demailly–Kollár’s important restriction formula on complex singularity exponents, and then we establish necessary conditions for the extremal case in the reformulated formula; we pose the subadditivity property on the complex singularity exponents of plurisubharmonic functions which is a generalization of Demailly–Kollár’s fundamental subadditivity property, and then we establish necessary conditions for the extremal case in the generalization. We also obtain two sharp relations on jumping numbers, introduce a new invariant of plurisubharmonic singularities and get its decreasing property for consecutive differences.

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Analysis and mathematical physics

Чжоу

Zhou

2020

Trudy Mat. Inst. Steklova

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В работе сначала напоминается контекст задачи об оптимальном $L^2$-продолжении, гипотезы Демайи о сильной открытости для пучков мультипликаторных идеалов и некоторых близких задач и существо наших недавних решений этих задач, а затем рассказывается о недавних результатах по смежным вопросам многомерного комплексного анализа и комплексной геометрии.

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A log Canonical Threshold Test

Abstract: In terms of log canonical threshold, we characterize plurisubharmonic functions with logarithmic asymptotical behaviour. 1 A direct proof was given later in [2].

Cited by 3 publications

References 27 publications

Recent Results in Several Complex Variables and Complex Geometry

Recent Results in Several Complex Variables and Complex Geometry

Restriction formula and subadditivity property related to multiplier ideal sheaves

Analysis and mathematical physics

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