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