On the supersingular K3 surface in characteristic 5 with Artin invariant 1

Abstract

We present three interesting projective models of the supersingular K3 surface X in characteristic 5 with Artin invariant 1. For each projective model, we determine smooth rational curves on X with the minimal degree and the projective automorphism group. Moreover, by using the superspecial abelian surface, we construct six sets of 16 disjoint smooth rational curves on X, and show that they form a beautiful configuration.

36 pages

References in corpus (3)

• The automorphism group of a supersingular K3 surface with Artin invariant 1 in characteristic 3
• A note on a supersingular K3 surface in characteristic 2
• An algorithm to compute automorphism groups of K3 surfaces and an application to singular K3 surfaces

Cited by in corpus (2)

• The graphs of Hoffman-Singleton, Higman-Sims, and McLaughlin, and the Hermitian curve of degree 6 in characteristic 5
• Projective models of the supersingular K3 surface with Artin invariant 1 in characteristic 5