Mordell-Weil groups and automorphism groups of elliptic K3 surfaces

TL;DR

This paper introduces a method to compute the action of Mordell-Weil groups on the Néron-Severi lattice of elliptic K3 surfaces and applies it to determine the automorphism group of a specific K3 surface related to a sextic curve.

Contribution

It provides a new computational approach to analyze the automorphism groups of elliptic K3 surfaces using Mordell-Weil group actions.

Findings

Computed a finite generating set for the automorphism group of a specific K3 surface.

Developed a method to calculate Mordell-Weil group actions on the Néron-Severi lattice.

Applied the method to a K3 surface birational to a double plane with a 6-cuspidal sextic curve.

Abstract

We present a method to calculate the action of the Mordell-Weil group of an elliptic K3 surface on the numerical N\'eron-Severi lattice of the K3 surface. As an application, we compute a finite generating set of the automorphism group of a K3 surface birational to the double plane branched along a 6-cuspidal sextic curve of torus type.