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

TL;DR

This paper determines the arithmetic nature of all 14 hypergeometric monodromy groups linked to Calabi-Yau threefolds, establishing that the last four are also arithmetic, completing the classification.

Contribution

It conclusively classifies all 14 hypergeometric monodromy groups as either arithmetic or thin, resolving a long-standing open problem.

Findings

4 additional groups are proven to be arithmetic

Total of 14 groups classified as arithmetic or thin

Completes the classification of these monodromy groups

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.