Arithmetic of singular Enriques Surfaces

Details Arithmetic of singular Enriques Surfaces Arithmetic of singular Enriques Surfaces

2010-02-08

arxiv.org/abs/1002.1598v2

Mathematics

Algebraic Geometry

32 pages; v2: Section 2 expanded, minor additions and edits

Scientific paper

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.

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