Asian Journal of Mathematics

Volume 8 (2004)

Number 3

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

Pages: 531 – 586

DOI: http://dx.doi.org/10.4310/AJM.2004.v8.n3.a8

Author

Ichiro Shimada

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 ℙ2 defined by ω2 = 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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