Malmendier, AndreasSchultz, Michael T.2023-01-112023-01-112022-01-011931-4523http://hdl.handle.net/10919/113128We use the mixed-twist construction of Doran and Malmendier to obtain a multi-parameter family of K3 surfaces of Picard rank ρ ≥ 16. Upon identifying a particular Jacobian elliptic fibration on its general member, we determine the lattice polarization and the Picard-Fuchs system for the family. We construct a sequence of restrictions that lead to extensions of the polarization by twoelementary lattices. We show that the Picard-Fuchs operators for the restricted families coincide with known resonant hypergeometric systems. Second, for the one-parameter mirror families of deformed Fermat hypersurfaces we show that the mixed-twist construction produces a non-resonant GKZ system for which a basis of solutions in the form of absolutely convergent Mellin-Barnes integrals exists whose monodromy we compute explicitlyPages 459-513application/pdfenIn CopyrightArticle - Refereed2023-01-11https://doi.org/10.4310/CNTP.2022.v16.n3.a21631931-4531