代数幾何学セミナー

過去の記録 ~05/28次回の予定今後の予定 05/29~

開催情報 金曜日 13:30~15:00 数理科学研究科棟(駒場) ハイブリッド開催/117号室
担当者 權業 善範、中村 勇哉、田中 公

2011年05月16日(月)

17:00-18:30   数理科学研究科棟(駒場) 126号室
大川 新之介 氏 (東京大学数理科学研究科)
On images of Mori dream spaces (JAPANESE)
[ 講演概要 ]
Mori dream space (MDS), introduced by Y. Hu and S. Keel, is a class of varieties whose geometry can be controlled via the VGIT of the Cox ring. It is a generalization of both toric varieties and log Fano varieties.

The purpose of this talk is to study the image of a morphism from a MDS.
Firstly I prove that such an image again is a MDS.
Secondly I introduce a fan structure on the effective cone of a MDS and show that the fan of the image coincides with the restriction of that of the source.

This fan encodes some information of the Zariski decompositions, which turns out to be equivalent to the information of the GIT equivalence. In toric case, this fan coincides with the so called GKZ decomposition.

The point is that these results can be clearly explained via the VGIT description for MDS.

If I have time, I touch on generalizations and an application to the Shokurov polytopes.