On the mixed-twist construction and monodromy of associated Picard-Fuchs systems

Abstract

We use the mixed-twist construction of Doran and Malmendier to obtain a multi-parameter family of K3 surfaces of Picard rank $\rho \ge 16$. 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 two-elementary 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 explicitly.

arXiv comment40 pages

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Cited by in corpus (2)

• On Néron-Severi lattices of Jacobian elliptic K3 surfaces
• On holomorphic conformal structures associated with lattice polarized K3 surfaces