K3 surfaces with 9 cusps in characteristic p

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Katsura, Toshiyuki¹  Schuett, Matthias^2,3 

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan

[2] Leibniz Univ Hannover, Inst Algebra Geometrie, Welfengarten 1, D-30167 Hannover, Germany

[3] Leibniz Univ Hannover, Riemann Ctr Geometry & Phys, Appelstr 2, D-30167 Hannover, Germany

关键词: K3 surface;    Cusp;    Abelian surface;    Supersingular;    Automorphism;   

DOI  :  10.1016/j.jpaa.2020.106558

来源: Elsevier

【 摘 要 】

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 not equal 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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free