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

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关于相关 Picard-Fuchs 系统的混合扭曲构造和单调性

我们使用 Doran 和 Malmendier 的混合扭曲构造来获得 Picard 秩 $\rho \geq 16$ 的多参数 K3 曲面族。在确定其一般成员上的特定雅可比椭圆纤维化后，我们确定了该族的晶格极化和 Picard-Fuchs 系统。我们构建了一系列限制，这些限制导致两个基本晶格的极化扩展。我们证明了受限族的 Picard-Fuchs 算子与已知的共振超几何系统一致。其次，对于变形费马超曲面的单参数镜像族，我们证明了混合扭曲构造产生了一个非共振 GKZ 系统，其中存在以绝对收敛梅林-巴恩斯积分形式存在的解的基础，我们明确计算其单态.