Arithmeticity of Four Hypergeometric Monodromy Groups associated to Calabi-Yau threefolds

Abstract

In [12], we show that 3 of the 14 hypergeometric monodromy groups associated to Calabi-Yau threefolds, are arithmetic. Brav-Thomas (in [3]) show that 7 of the remaining 11, are thin. In this article, we settle the arithmeticity problem for the 14 monodromy groups, by showing that, the remaining 4 are arithmetic.

Referees' suggestions have been included, to appear in International Mathematics Research Notices (IMRN)

References in corpus (2)

• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Some monodromy groups of finite index in $S{p}_4(\mathbb{Z})$

Cited by in corpus (9)

• Finiteness and the Emergence of Dualities
• Zariski Density and Computing in Arithmetic Groups
• Experimenting with symplectic hypergeometric monodromy groups
• On Orthogonal Hypergeometric Groups of Degree Five
• Hodge Numbers from Picard-Fuchs Equations
• Symplectic Hypergeometric Groups of Degree Six
• Orthogonal Hypergeometric Groups with a Maximally Unipotent Monodromy
• Thin monodromy in $\mathrm{Sp}(4)$ and $\mathrm{Sp}(6)$
• Commensurability and arithmetic equivalence for orthogonal hypergeometric monodromy groups