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

Ichiro Shimada
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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 $w^2=G$. 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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Ichiro Shimada. 2003-11-06. Supersingular K3 surfaces in characteristic 2 as double covers of a projective plane. https://arxiv.org/abs/math/0311073

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