Kummer surfaces in characteristic two
by
Stefan Schröer
Mathematisches Institut, Heinrich-Heine-Univerität, 40225 Duesseldorf, Germany

The classical Kummer construction attaches to each abelian surface a K3 surface. As Shioda and Katsura showed, this construction breaks down for supersingular abelian surfaces in characteristic two. Replacing supersingular abelian surfaces by the selfproduct of the rational cuspidal curve, and the sign involution by suitable infinitesimal group scheme actions, I give a new Kummer-type construction in characteristic two. We encounter rational double points of type D₄ and D₈, instead of A₁. The resulting surfaces are supersingular K3 surfaces with Artin invariant one and two.

Date received: February 27, 2005