## 代数幾何学セミナー

開催情報 火曜日　10:30～11:30 or 12:00　数理科学研究科棟(駒場) ハイブリッド開催/002号室 權業 善範・中村 勇哉・田中公

### 2018年05月21日(月)

15:30-17:00   数理科学研究科棟(駒場) 122号室

Christopher Hacon 氏 (Utah/Kyoto)
Towards the termination of flips. (English)
[ 講演概要 ]
The minimal model program (MMP) predicts that if $X$ is a smooth complex projective variety which is not uniruled, then there is a finite sequence of "elementary" birational maps
$X=X_0-->X_1-->X_2-->...-->X_n$ known as divisorial contractions and flips whose output $\bar X=X_n$ is a minimal model so that $K_{\bar X}$ is a nef $Q$-divisor i.e it intersects all curves $C\subset \bar X$ non-negatively: $K_{\bar X}\cdot C\geq 0$.
The existence of these birational maps has been established, but in order to complete the MMP, it is necessary to show that flips terminate i.e. there are no infinite sequences of flips. In this talk we will discuss recent results towards the termination of flips.
[ 参考URL ]
https://www.math.utah.edu/~hacon/