Algebra & Number Theory

Arithmetic of singular Enriques surfaces

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 $H(d)$. Our main theorem is that the same holds true for any Enriques quotient of $X$. It is based on a study of Néron–Severi groups of singular K3 surfaces. We also comment on Galois actions on divisors of Enriques surfaces.

Article information

Source
Algebra Number Theory, Volume 6, Number 2 (2012), 195-230.

Dates
Revised: 28 November 2010
Accepted: 29 December 2010
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513729776

Digital Object Identifier
doi:10.2140/ant.2012.6.195

Mathematical Reviews number (MathSciNet)
MR2950152

Zentralblatt MATH identifier
1248.14043

Citation

Hulek, Klaus; Schütt, Matthias. Arithmetic of singular Enriques surfaces. Algebra Number Theory 6 (2012), no. 2, 195--230. doi:10.2140/ant.2012.6.195. https://projecteuclid.org/euclid.ant/1513729776

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