## Algebraic Geometry Seminar

Seminar information archive ～03/19｜Next seminar｜Future seminars 03/20～

Date, time & place | Tuesday 15:30 - 17:00 Room #122 (Graduate School of Math. Sci. Bldg.) |
---|

### 2018/05/21

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Towards the termination of flips. (English)

https://www.math.utah.edu/~hacon/

**Christopher Hacon**(Utah/Kyoto)Towards the termination of flips. (English)

[ Abstract ]

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.

[ Reference URL ]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.

https://www.math.utah.edu/~hacon/