K3 surfaces with 9 cusps in characteristic p

authored by

Toshiyuki Katsura, Matthias Schütt

Abstract

We study K3 surfaces with 9 cusps, i.e. 9 disjoint A 2 configurations of smooth rational curves, over algebraically closed fields of characteristic p≠3. Much like in the complex situation studied by Barth, we prove that each such surface admits a triple covering by an abelian surface. Conversely, we determine which abelian surfaces with order three automorphisms give rise to K3 surfaces. We also investigate how K3 surfaces with 9 cusps hit the supersingular locus.

Organisation(s)

Institut für Algebraische Geometrie
Riemann Center for Geometry and Physics

External Organisation(s)

Tokyo University of Technology

Type

Artikel

Journal

Journal of Pure and Applied Algebra

Volume

225

No. of pages

17

ISSN

0022-4049

Publication date

04.2021

Publication status

Veröffentlicht

Peer reviewed

Yes

Electronic version(s)

https://arxiv.org/abs/1902.01579 (Access: Offen)
https://doi.org/10.1016/j.jpaa.2020.106558 (Access: Geschlossen)