A 1-Dimensional Family of Enriques Surfaces in Characteristic 2 Covered by the Supersingular K3 Surface with Artin Invariant 1

摘要

We give a 1-dimensional family of classical and super singular Enriques surfaces in characteristic 2 covered by the super singular K3 surface with Artin invariant 1. Moreover we show that there exist thirty nonsingular rational curves and ten non-effective (-2)-divisors on these Enriques surfaces whose reflection group is of finite index in the orthogonal group of the Neron-Severi lattice modulo torsion.