# Geometry and Arithmetic

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#### pp: 243–255

#### DOI: 10.4171/119-1/14

^{[1]}and Shigeyuki Kondō

^{[2]}(1) Hosei University, Tokyo, Japan

(2) Nagoya University, Japan

We construct, on a supersingular K3 surface with Artin invariant 1 in characteristic 2, a set of 21 disjoint smooth rational curves and another set of 21 disjoint smooth rational curves such that each curve in one set intersects exactly 5 curves from the other set with multiplicity 1 by using the structure of a generalized Kummer surface. As a corollary we have a concrete construction of a K3 surface with 21 rational double points of type A1 in characteristic 2.

*Keywords: *Supersingular K3 surface, Artin invariant, characteristic 2, Néron–Severi group, generalized Kummer surface