Arithmetic of singular Enriques Surfaces
Algebraic Geometry
2011-01-04 v2 Number Theory
Abstract
We study the arithmetic of Enriques surfaces whose universal covers are singular K3 surfaces. If a singular K3 surface X has discriminant d, then it has a model over the ring class field d. Our main theorem is that the same holds true for any Enriques quotient of X. It is based on a study on Neron-Severi groups of singular K3 surfaces. We also comment on Galois actions on divisors of Enriques surfaces.
Cite
@article{arxiv.1002.1598,
title = {Arithmetic of singular Enriques Surfaces},
author = {Klaus Hulek and Matthias Schuett},
journal= {arXiv preprint arXiv:1002.1598},
year = {2011}
}
Comments
32 pages; v2: Section 2 expanded, minor additions and edits