Jacobian elliptic fibrations on the generalized Inose quartic of Picard rank sixteen

TL;DR

This paper studies a family of complex K3 surfaces with specific lattice properties, showing that a general surface admits exactly four distinct Jacobian elliptic fibrations and providing explicit constructions for these fibrations.

Contribution

It identifies and explicitly constructs all Jacobian elliptic fibrations on a generalized Inose quartic K3 surface with Picard rank sixteen.

Findings

A general member admits exactly four inequivalent Jacobian elliptic fibrations.

Explicit pencils for each of the four fibrations are constructed.

The work extends understanding of elliptic fibrations on K3 surfaces with specific lattice structures.

Abstract

We consider the family of complex algebraic K3 surfaces $\mathcal{X}$ with Picard lattice containing the unimodular lattice $H \oplus E_7(-1) \oplus E_7(-1)$. The surface $\mathcal{X}$ admits a birational model isomorphic to a quartic hypersurface that generalizes the Inose quartic. We prove that a general member of this family admits exactly four inequivalent Jacobian elliptic fibrations and construct explicit pencils for them.