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代数幾何学セミナー
過去の記録 ～09/11｜次回の予定｜今後の予定 09/12～
| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) 118号室 |
|---|---|
| 担当者 | 權業 善範、河上 龍郎 、榎園 誠 |
2026年10月02日(金)
10:30-12:00 数理科学研究科棟(駒場) 122号室
いつもと時間帯・部屋が異なります。
JongHae Keum 氏 (KIAS)
Automorphisms of Fermat quartic surface
いつもと時間帯・部屋が異なります。
JongHae Keum 氏 (KIAS)
Automorphisms of Fermat quartic surface
[ 講演概要 ]
In 1944 Beniamino Segre proved that the Fermat quartic surface in the 3-dimensional projective space has infinitely many discrete automorphisms. It was the first example of an algebraic surface with infinite discrete automorphism group. Since then, it has long been an open problem to find generators of its automorphism group.
On the other hand, any other Fermat hypersurface of dimension > 1 and degree > 2 admits only projectively linear automorphisms, and has finite automorphism group.
With Keiji Oguiso and Xun Yu, we solve this problem, finding 16 geometric generators of finite order.
I will present this result, along with history of computation of automorphism groups of other K3 surfaces.
In 1944 Beniamino Segre proved that the Fermat quartic surface in the 3-dimensional projective space has infinitely many discrete automorphisms. It was the first example of an algebraic surface with infinite discrete automorphism group. Since then, it has long been an open problem to find generators of its automorphism group.
On the other hand, any other Fermat hypersurface of dimension > 1 and degree > 2 admits only projectively linear automorphisms, and has finite automorphism group.
With Keiji Oguiso and Xun Yu, we solve this problem, finding 16 geometric generators of finite order.
I will present this result, along with history of computation of automorphism groups of other K3 surfaces.
