Rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3

2011/07/08 by Katsura, Toshiyuki, Kondo, Shigeyuki
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1107.1543

Abstract

We show the existence of 112 non-singular rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3 by several ways. Using these rational curves, we have a (16)₁₀-configuration and a (280₄, 112₁₀)-configuration on the K3 surface. Moreover we study the Picard lattice by using the theory of the Leech lattice. The 112 non-singular rational curves correspond to 112 Leech roots.

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