Supersingular K3 surfaces in characteristic 2 as double covers of a projective plane

2003/11/06 by Ichiro Shimada, Shimada, Ichiro
Mathematics · #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG #msc:14J28

paper · pdf · doi:10.48550/arxiv.math/0311073

54 pages, 5 figures

arxiv created 2003/11/06 · openalex publication_date 2003/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every supersingular K3 surface X in characteristic 2, there exists a homogeneous polynomial G of degree 6 such that X is birational to the purely inseparable double cover of a projective plane defined by w²=G. We present an algorithm to calculate from G a set of generators of the numerical Néron-Severi lattice of X. As an application, we investigate the stratification defined by the Artin invariant on a moduli space of supersingular K3 surfaces of degree 2 in characteristic 2.

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