$\mathbb Q$-bases of the Néron–Severi groups of certain elliptic surfaces

Masamichi Kuroda

Vol. 273 (2015), No. 1, 101–121

DOI: 10.2140/pjm.2015.273.101

Abstract

P. Stiller computed the rank of the Néron–Severi group (known as the Picard number) for several families of elliptic surfaces. However, he did not give the generators of these groups. In this paper we give $\mathbb{Q}$-bases of these groups explicitly. If these surfaces are rational, we also show that they are $\mathbb{Z}$-bases.

Keywords

elliptic surfaces, Néron–Severi groups

Mathematical Subject Classification 2010

Primary: 14J27

Milestones

Received: 23 September 2013

Accepted: 15 January 2014

Published: 6 December 2014