Vol. 6, No. 2, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 10, 1767–1943
Issue 9, 1589–1766
Issue 8, 1403–1587
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
Arithmetic of singular Enriques surfaces

Klaus Hulek and Matthias Schütt

Vol. 6 (2012), No. 2, 195–230
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.

Dedicated to the memory of Eckart Viehweg

Keywords
Enriques surface, singular K3 surface, elliptic fibration, Néron–Severi group, Mordell–Weil group, complex multiplication
Mathematical Subject Classification 2000
Primary: 14J28
Secondary: 11E16, 11G15, 11G35, 14J27
Milestones
Received: 13 March 2010
Revised: 28 November 2010
Accepted: 29 December 2010
Published: 24 June 2012
Authors
Klaus Hulek
Institut für Algebraische Geometrie
Leibniz Universität Hannover
Welfengarten 1
30167 Hannover
Germany
Matthias Schütt
Institut für Algebraische Geometrie
Leibniz Universität Hannover
Welfengarten 1
30167 Hannover
Germany