Vol. 273, No. 1, 2015

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

Masamichi Kuroda

Vol. 273 (2015), No. 1, 101–121
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 -bases of these groups explicitly. If these surfaces are rational, we also show that they are -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
Authors
Masamichi Kuroda
Department of Mathematics
Hokkaido University
Sapporo 060-0810
Japan