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

2012/01/22 by Ichiro Shimada, Shimada, Ichiro · 1 citation
Mathematics · #14G17 #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG #msc:14G17 #msc:14J28

paper · pdf · doi:10.48550/arxiv.1201.4533

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

openalex publication_date 2012/01/22 · arxiv created 2013/12/14 · arxiv updated 2013/12/17 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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.

Citations

• A note on a supersingular K3 surface in characteristic 2
• On the supersingular K3 surface in characteristic 5 with Artin invariant 1

Cited by

• K3 surfaces of degree six arising from desmic tetrahedra

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