## Algebraic Geometry Seminar

Seminar information archive ～10/10｜Next seminar｜Future seminars 10/11～

Date, time & place | Friday 13:30 - 15:00 ハイブリッド開催/117Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.) |
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Organizer(s) | GONGYO Yoshinori, NAKAMURA Yusuke, TANAKA Hiromu |

### 2014/06/02

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

On base point free theorem for log canonical three folds over the algebraic closure of a finite field (JAPANESE)

**Yusuke Nakamura**(University of Tokyo)On base point free theorem for log canonical three folds over the algebraic closure of a finite field (JAPANESE)

[ Abstract ]

We will discuss about the base point free theorem on three-dimensional

pairs defined over the algebraic closure of a finite field.

We know the base point free theorem on arbitrary-dimensional Kawamata

log terminal pairs in characteristic zero. By Birkar and Xu, the base

point free theorem in positive characteristic is known for big line

bundles on three-dimensional Kawamata log terminal pairs defined over

an algebraically closed field of characteristic larger than 5. Over the

algebraic closure of a finite field, a stronger result was proved by Keel.

The purpose of this talk is to generalize the Keel's result. We will

prove the base point free theorem for big line bundles on

three-dimensional log canonical pairs defined over the algebraic closure

of a finite field. This theorem is not valid for another field.

This is joint work with Diletta Martinelli and Jakub Witaszek.

We will discuss about the base point free theorem on three-dimensional

pairs defined over the algebraic closure of a finite field.

We know the base point free theorem on arbitrary-dimensional Kawamata

log terminal pairs in characteristic zero. By Birkar and Xu, the base

point free theorem in positive characteristic is known for big line

bundles on three-dimensional Kawamata log terminal pairs defined over

an algebraically closed field of characteristic larger than 5. Over the

algebraic closure of a finite field, a stronger result was proved by Keel.

The purpose of this talk is to generalize the Keel's result. We will

prove the base point free theorem for big line bundles on

three-dimensional log canonical pairs defined over the algebraic closure

of a finite field. This theorem is not valid for another field.

This is joint work with Diletta Martinelli and Jakub Witaszek.