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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)
Institute of Algebraic Geometry
Riemann Center for Geometry and Physics
External Organisation(s)
Hosei University
Type
Article
Journal
Journal of Pure and Applied Algebra
Volume
225
No. of pages
17
ISSN
0022-4049
Publication date
04.2021
Publication status
Published
Peer reviewed
Yes
Electronic version(s)
https://arxiv.org/abs/1902.01579 (Access: Open)
https://doi.org/10.1016/j.jpaa.2020.106558 (Access: Closed)