用Riemann-Roch定理证明最小对数偏差的有界性
Towards boundedness of minimal log discrepancies by Riemann--Roch theorem
摘要：
利用Riemann-Roch定理讨论了定维最小对数偏差的有界性问题。在将其归结为Gorenstein终端奇点的情形后，首先证明了当重数或嵌入维数有界时，其最小对数偏差有界。其次，我们恢复的Gorenstein终端三重奇异里德的特性，其最小的日志差异的精确边界Markushevich，没有明确的分类。最后给出了一般超平面截面具有一个终端段的四重奇点的精确边界。
英文摘要：
We introduce an approach of Riemann--Roch theorem to the boundedness problem of minimal log discrepancies in fixed dimension. After reducing it to the case of a Gorenstein terminal singularity, firstly we prove that its minimal log discrepancy is bounded if either multiplicity or embedding dimension is bounded. Secondly we recover the characterisation of a Gorenstein terminal three-fold singularity by Reid, and the precise boundary of its minimal log discrepancy by Markushevich, without explicit classification. Finally we provide the precise boundary for a special four-fold singularity, whose general hyperplane section has a terminal piece.
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