Maximal families of Calabi-Yau manifolds with minimal length Yukawa coupling

TL;DR

The paper constructs maximal families of Calabi-Yau manifolds with minimal Yukawa coupling length for odd dimensions, confirming Shafarevich's conjecture and linking to Shimura varieties and arithmetic ball quotients.

Contribution

It explicitly exhibits maximal families of Calabi-Yau manifolds with Yukawa length one for all odd dimensions n ≥ 3, and relates these to Shimura and arithmetic ball quotients.

Findings

Yukawa coupling length is one for the constructed families.

Shafarevich's conjecture holds for these families.

Connections to Shimura varieties and arithmetic ball quotients.

Abstract

For each natural odd number $n\geq 3$, we exhibit a maximal family of $n$-dimensional Calabi-Yau manifolds whose Yukawa coupling length is one. As a consequence, Shafarevich's conjecture holds true for these families. Moreover, it follows from Deligne-Mostow and Mostow that, for $n=3$, it can be partially compactified to a Shimura family of ball type, and for $n=5,9$, there is a sub $\mathbb Q$-PVHS of the family uniformizing a Zariski open subset of an arithmetic ball quotient.