学术报告（陈亦飞 10.13）

Abstract：

Singularities is an important topic in algebraic geometry. In the higher dimensional minimal model program (MMP), singularities naturally appear. People are interested in the behavior of singularities under the fundamental operations in MMP, such as extremal contraction. There are three kinds of extremal contractions: divisorial contraction, flips and Mori fiber space. For the first two cases, singularities will not be worse. However, for Mori fiber spaces, singularities can be worse. There are two conjectures for the singularities of Mori fiber spaces, McKernan Conjecture and a more general conjecture of Shokurov, which roughly say the singularities of Mori fiber spaces can be under controlled. In a joint work with Caucher Birkar, we study the toric case of Shokurov Conjecture, and get some interesting applications.