JACOBIAN ELLIPTIC FIBRATIONS ON THE GENERALIZED INOSE QUARTIC OF PICARD RANK SIXTEEN

Abstract

We consider the family of complex algebraic K3 surfaces 𝒳 with Picard lattice containing the unimodular lattice H⊕E7(−1)⊕E7(−1). The surface 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.