Two two-dimensional terminations
Two two-dimensional terminations
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DOI：
10.1215/s0012-7094-93-06922-0
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发表时间：
1992-06
影响因子：
2.5
通讯作者：
V. Alexeev
中科院分区：
文献类型：
--
作者：
V. Alexeev
在最小模型程序中考虑了具有对数终端和对数正则奇点的品种，见\cite{.}用于介绍。在\cite{shokurov：hyp}中，许多有趣的集合，与这些变种相关联，有一些共同之处：它们满足升链条件，这意味着每一个增加的元素链终止。从哲学上讲，这就是为什么最小模型程序中的两个主要假设：翻转的存在和终止应该是真的，并且可以证明。本文证明了下列两个集合满足升链条件：1. $K_X+B$的最小对数差集，其中$X$是具有对数正则奇点的曲面。2.组$（b_1，. B_s）$使得存在一个曲面$X$具有对数正则和数值平凡$K_X+\sum B_j B_j$。这类群的序是以自然的方式定义的。
Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see \cite{...} for introduction. In \cite{shokurov:hyp} it was conjectured that many of the interesting sets, associated with these varieties have something in common: they satisfy the ascending chain condition, which means that every increasing chain of elements terminates. Philosophically, this is the reason why two main hypotheses in the Minimal Model Program: existence and termination of flips should be true and are possible to prove. In this paper we prove that the following two sets satisfy the ascending chain condition: 1. The set of minimal log discrepancies for $K_X+B$ where $X$ is a surface with log canonical singularities. 2. The set of groups $(b_1,...b_s)$ such that there is a surface $X$ with log canonical and numerically trivial $K_X+\sum b_jB_j$. The order on such groups is defined in a natural way.