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

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.

arXiv comment16 pages. arXiv admin note: substantial text overlap with arXiv:2009.09635