We present a method to calculate the action of the Mordell–Weil group of an elliptic surface on the numerical Néron–Severi lattice of the surface. As an application, we compute a finite generating set of the automorphism group of a surface birational to the double plane branched along a 6-cuspidal sextic curve of torus type.
Cite this article
I. Shimada, Mordell–Weil groups and automorphism groups of elliptic surfaces. Rev. Mat. Iberoam. (2023), published online firstDOI 10.4171/RMI/1449