The Classification of Rigid Torus Quotients with Canonical Singularities in Dimension Three

TL;DR

This paper classifies three-dimensional torus quotients with isolated canonical singularities, enriching the understanding of their structure and relation to Calabi-Yau 3-folds with Gorenstein singularities.

Contribution

It provides a detailed classification of rigid 3D torus quotients with canonical singularities, extending previous work on Calabi-Yau 3-folds.

Findings

Classification up to biholomorphism and diffeomorphism

Identification of canonical singularities in these quotients

Relation to Calabi-Yau 3-folds of type III_0

Abstract

We provide a fine classification of rigid three-dimensional torus quotients with isolated canonical singularities, up to biholomorphism and diffeomorphism. This complements the classification of Calabi-Yau 3-folds of type $\rm{III}_0$, which are those quotients with Gorenstein singularities.