English

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.

Keywords

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

R2 v1 2026-06-21T14:44:33.213Z