都の西北代数幾何学セミナー

日程：2026年 5月 22日（金）16:30 - 18:00（+ 10分 質疑応答）

教室：早稲田大学 西早稲田キャンパス 51号館 18-08

講演者：高田 佑太 氏（東京大学）

タイトル：Gap theorems and achirality for automorphisms of K3 surfaces and Enriques surfaces

アブストラクト：
For a group and a norm on the group, a gap theorem asserts that the stabilization of the norm of each element is either zero or bounded below by a positive constant. In this talk, we show such a gap theorem for the automorphism group of a K3 surface or an Enriques surface with respect to the entropy norm, which measures the minimal number of zero-entropy automorphisms required to express a given automorphism. On the other hand, an element of a group is said to be achiral if some positive power is conjugate to its inverse. The gap theorem yields a criterion for the achirality of positive-entropy automorphisms. We further study the achirality of zero-entropy automorphisms in terms of genus-one fibrations. This is a joint work with Kohei Kikuta and Taiki Takatsu. 

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