Projective models of the supersingular K3 surface with Artin invariant 1 in characteristic 5

Abstract

Let X be a supersingular K3 surface in characteristic 5 with Artin invariant 1. Then X has a polarization that realizes X as the Fermat sextic double plane. We present a list of polarizations of X with degree 2 whose intersection number with this Fermat sextic polarization is less than or equal to 5, and give the defining equations of the corresponding projective models. We also present a method to describe birational morphisms between these projective models explicitly. As a by-product, a non-projective automorphism of the Fermat sextic double plane is obtained.

25 pages, no figures. New references are added. Some tables are omitted

References in corpus (4)

• Elliptic fibrations on a generic Jacobian Kummer surface
• 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
• On the supersingular K3 surface in characteristic 5 with Artin invariant 1

Cited by in corpus (2)

• The automorphism group of a supersingular K3 surface with Artin invariant 1 in characteristic 3
• On certain duality of Néron-Severi lattices of supersingular K3 surfaces