正特徵數中的極小模型理論

Abstract

本文分為兩個部分。第一個部分介紹極小模型理論是如何運作的，尤其是在正特徵數的時候。第二個部分，Mori 在特徵數零時對三維 terminal 奇點的分類中，我確定了大部分在正特徵數時，仍然會是 terminal 奇點。

In this thesis, there are two parts. The first part is to introduce what the minimal model program (MMP) is and how it works, especially in positive characteristic. Also, I illustrate some differences between characteristic zero and positive characteristic. In the second part, I verify that the classification Mori gave in characteristic zero for the terminal singularities in dimension 3 is mostly true in positive characteristic.