An Enriques involution of a supersingular K3 surface over odd characteristic
Algebraic Geometry
2013-01-15 v3 Number Theory
Abstract
In this paper, we prove, as the complex case, a supersingular K3 surface over a field of odd characteristic has an Enriques involution if and only if there exists a primitive embedding of the twice of the Enriques lattice into the Neron-Severi group such that the orthogonal complement of the embedding has no vector of self-intersection -2 using the Crystalline Torelli theorem. By this criterion and some lattice calculation, we prove that when the characteristic of the base field is p=19 or p>23, a superingular K3 surface is an Enriques K3 surface if and only if the Artin invariant is less than 6.
Keywords
Cite
@article{arxiv.1301.1118,
title = {An Enriques involution of a supersingular K3 surface over odd characteristic},
author = {Junmyeong Jang},
journal= {arXiv preprint arXiv:1301.1118},
year = {2013}
}