A sharp lower bound for the log canonical threshold
A sharp lower bound for the log canonical threshold
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DOI：
10.1007/s11511-014-0107-4
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发表时间：
2012-01
期刊：
影响因子：
3.7
通讯作者：
J. Demailly;H. H. Phạm-H.
中科院分区：
文献类型：
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作者：
J. Demailly;H. H. Phạm-H.
在这篇注记中，我们证明了在的开子集上具有孤立奇点的多重亚调和函数的对数正则门限的一个精确的下界。这个门限被定义为在0的邻域上可积的常数0的上确界。我们涉及到中间重数，定义为0的Lelong数(因此特别是)。我们的主要结果是。这个不等式被证明是尖锐的；它同时改进了由于Skoda的经典结果，以及近年来在双曲面几何中得到关键应用的较低估计。证明在于归结为环面情形，即由单项理想产生的奇点。
In this note, we prove a sharp lower bound for the log canonical threshold of a plurisubharmonic functionwith an isolated singularity at 0 in an open subset of. This threshold is defined as the supremum of constantsc> 0 such thatis integrable on a neighborhood of 0. We relateto the intermediate multiplicity numbers, defined as the Lelong numbers ofat 0 (so that in particular). Our main result is that. This inequality is shown to be sharp; it simultaneously improves the classical resultdue to Skoda, as well as the lower estimatewhich 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.