A sharp lower bound for the log canonical threshold
成果类型：
Article
署名作者：
Demailly, Jean-Pierre; Hoang Hiep Pham
署名单位：
Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Hanoi National University of Education
刊物名称：
ACTA MATHEMATICA
ISSN/ISSBN：
0001-5962
DOI：
10.1007/s11511-014-0107-4
发表日期：
2014
页码：
1-9
关键词：
摘要：
In this note, we prove a sharp lower bound for the log canonical threshold of a plurisubharmonic function with an isolated singularity at 0 in an open subset of . This threshold is defined as the supremum of constants c > 0 such that is integrable on a neighborhood of 0. We relate to the intermediate multiplicity numbers , defined as the Lelong numbers of at 0 (so that in particular ). Our main result is that . This inequality is shown to be sharp; it simultaneously improves the classical result due to Skoda, as well as the lower estimate which has received crucial applications to birational geometry in recent years. The proof consists in a reduction to the toric case, i.e. singularities arising from monomial ideals.
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