Pure and Applied Mathematics Quarterly

Volume 11 (2015)

Number 4

Special Issue: In Honor of Eduard Looijenga, Part 1 of 3

Guest Editor: Gerard van der Geer

A $1$-dimensional family of Enriques surfaces in characteristic $2$ covered by the supersingular $K3$ surface with Artin invariant $1$

Pages: 683 – 709

DOI: http://dx.doi.org/10.4310/PAMQ.2015.v11.n4.a6

Authors

Toshiyuki Katsura (Faculty of Science and Engineering, Hosei University, Koganei-shi, Tokyo, Japan)

Shigeyuki Kondō (Graduate School of Mathematics, Nagoya University, Nagoya, Japan)

Abstract

We give a $1$-dimensional family of classical and supersingular Enriques surfaces in characteristic $2$ covered by the supersingular $K3$ 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 Néron–Severi lattice modulo torsion.

Keywords

Enriques surface, $K3$ surface, classical, supersingular

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