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代数幾何学セミナー
過去の記録 ～04/25｜次回の予定｜今後の予定 04/26～
| 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 |
2022年12月21日(水)
13:00-14:00 or 14:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
いつもと部屋が異なります. 京大代数幾何セミナーと共催です.
Hsueh-Yung Lin 氏 (NTU)
Towards a geometric origin of the dynamical filtrations (English)
いつもと部屋が異なります. 京大代数幾何セミナーと共催です.
Hsueh-Yung Lin 氏 (NTU)
Towards a geometric origin of the dynamical filtrations (English)
[ 講演概要 ]
Let X be a smooth projective variety with an automorphism f. When X is a threefold, Serge Cantat asked whether X has a non-trivial equivariant rational fibration, if the action of f on the Néron-Severi space is non-trivial and unipotent. We will propose a precise conjecture related to Cantat's question for minimal varieties in arbitrary dimension, in light of the "dynamical filtrations" arising in the study of zero entropy group actions. This conjecture also suggests a geometric origin of dynamical filtrations, whose definition is purely cohomological. We will provide some heuristic evidence from the relative abundance conjecture.
If time permits, we will also explain how the study of dynamical filtrations leads to new results about solvable group actions, which are not necessarily of zero entropy.
Let X be a smooth projective variety with an automorphism f. When X is a threefold, Serge Cantat asked whether X has a non-trivial equivariant rational fibration, if the action of f on the Néron-Severi space is non-trivial and unipotent. We will propose a precise conjecture related to Cantat's question for minimal varieties in arbitrary dimension, in light of the "dynamical filtrations" arising in the study of zero entropy group actions. This conjecture also suggests a geometric origin of dynamical filtrations, whose definition is purely cohomological. We will provide some heuristic evidence from the relative abundance conjecture.
If time permits, we will also explain how the study of dynamical filtrations leads to new results about solvable group actions, which are not necessarily of zero entropy.
