Some monodromy groups of finite index in $S{p}_4(\mathbb{Z})$

Abstract

We determine the index of five of the $7$ hypergeometric Calabi-Yau operators that have finite index in $S{p}_4(\mathbb{Z})$ and in two cases give a complete description of the monodromy group. Furthermore we found six non-hypergeometric Calabi-Yau operators with finite index in $S{p}_4(\mathbb{Z})$, most notably a case where the index is one.

14 pages, 1 figure

References in corpus (2)

• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Algebraic characterization of differential operators of Calabi-Yau type

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• On Orthogonal Hypergeometric Groups of Degree Five
• Experimenting with symplectic hypergeometric monodromy groups
• Constructive Membership Tests in Some Infinite Matrix Groups
• Commensurability and arithmetic equivalence for orthogonal hypergeometric monodromy groups
• Orthogonal Hypergeometric Groups with a Maximally Unipotent Monodromy