Crystallographic Groups and Calabi-Yau 3-folds of Type $\mathrm{III}_0$

TL;DR

This paper classifies certain Gorenstein quotients of 3D abelian varieties with isolated singularities, refining previous results on fibred Calabi-Yau threefolds using crystallographic group theory methods.

Contribution

It provides a detailed classification of these quotients up to biholomorphism and homeomorphism, advancing the understanding of Calabi-Yau threefolds of type III_0.

Findings

Refined classification of Gorenstein quotients of abelian varieties

Application of crystallographic group theory to orbifold fundamental groups

Enhanced understanding of fibred Calabi-Yau threefolds of type III_0

Abstract

We provide a fine classification of Gorenstein quotients of three-dimensional abelian varieties with isolated singularities, up to biholomorphism and homeomorphism. This refines a result of Oguiso and Sakurai about fibred Calabi-Yau threefolds of type $\mathrm{III}_0$. Our proof relies on methods of crystallographic group theory applied to the orbifold fundamental groups of such quotients.