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

Abstract

P. Stiller computed the Picard numbers of several families of elliptic surfaces, the rank of the Néron-Severi groups of these 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, then we also show that they are $\mathbb{Z}$-bases.

arXiv comment19 pages