On N\'eron-Severi lattices of Jacobian elliptic K3 surfaces

TL;DR

This paper classifies Jacobian elliptic fibrations on K3 surfaces with specific automorphism and Mordell-Weil group properties, providing detailed lattice-theoretic multiplicities for each case.

Contribution

It offers a comprehensive classification of Jacobian elliptic fibrations on K3 surfaces with finite automorphism groups and those with finite Mordell-Weil groups on surfaces with infinite automorphism groups and 2-elementary Néron-Severi lattices.

Findings

Complete classification of fibrations with finite automorphism groups.

Classification of fibrations with finite Mordell-Weil groups on specific K3 surfaces.

Calculation of lattice-theoretic multiplicities for all classified fibrations.

Abstract

We classify all Jacobian elliptic fibrations on K3 surfaces with finite automorphism group. We also classify all Jacobian elliptic fibrations with finite Mordell-Weil group on K3 surfaces with infinite automorphism group and 2-elementary N\'eron-Severi lattice. As part of the classification, we compute the lattice theoretic multiplicities of all Jacobian elliptic fibrations in both cases.