Algebraic Geometry Seminar

Seminar information archive ~06/23Next seminarFuture seminars 06/24~

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.)
Organizer(s) GONGYO Yoshinori, NAKAMURA Yusuke, TANAKA Hiromu

2022/12/21

13:00-14:00 or 14:30   Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
The room is different from the usual place. This is a joint seminar with Kyoto University.
Hsueh-Yung Lin (NTU)
Towards a geometric origin of the dynamical filtrations (English)
[ Abstract ]
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.