Text only print
Full screen print
Algebraic Geometry Seminar
Seminar information archive ～09/11｜Next seminar｜Future seminars 09/12～
| Date, time & place | Friday 13:30 - 15:00 118Room #118 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | GONGYO Yoshinori, KAWAKAMI Tatsuro, ENOKIZONO Makoto |
2026/10/02
10:30-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)
JongHae Keum (KIAS)
Automorphisms of Fermat quartic surface
JongHae Keum (KIAS)
Automorphisms of Fermat quartic surface
[ Abstract ]
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.
