BooksecrCollected Volumepp. 243–255

A note on a supersingular K3 surface in characteristic 2

  • Toshiyuki Katsura

    Hosei University, Tokyo, Japan

  • Shigeyuki Kondō

    Nagoya University, Japan
A note on a supersingular K3 surface in characteristic 2 cover
Download Chapter PDF

A subscription is required to access this book chapter.

Abstract

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.