INTRODUCTION TO THE TORIC MORI THEORY
INTRODUCTION TO THE TORIC MORI THEORY
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DOI：
10.1307/mmj/1100623418
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发表时间：
2003-07
影响因子：
0.9
通讯作者：
O. Fujino;H. Sato
中科院分区：
文献类型：
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作者：
O. Fujino;H. Sato
本文的主要目的是给出复曲面Mori理论的一个简单的非组合证明。在这里，复曲面Mori理论是指复曲面品种的（log）最小模型程序（MMP，简称）。我们尽量减少球迷和他们的分解的参数。我们向以下人员推荐本文：（A）那些对操作风扇及其分解感到不舒服的人，（B）那些熟悉复曲面几何但不熟悉MMP的人。范畴（A）中的人将从几个问题的冗长的组合论证中解脱出来。属于（B）类的人将发现复曲面森理论的潜力。作为应用，我们讨论了复曲面簇上的Zapriki分解和非退化超曲面奇点的部分分解。通过这些应用，读者将学会使用Toric Mori理论。
The main purpose of this paper is to give a simple and non-combinatorial proof of the toric Mori theory. Here, the toric Mori theory means the (log) Minimal Model Program (MMP, for short) for toric varieties. We minimize the arguments on fans and their decompositions. We recommend this paper to the following people: (A) those who are uncomfortable with manipulating fans and their decompositions, (B) those who are familiar with toric geometry but not with the MMP. People in the category (A) will be relieved from tedious combina- torial arguments in several problems. Those in the category (B) will discover the potential of the toric Mori theory. As applications, we treat the Zariski decomposition on toric varieties and the partial resolutions of non-degenerate hypersurface singularities. By these applications, the reader will learn to use the toric Mori theory.