# Finite quotients of three-dimensional complex tori

## TL;DR

This paper characterizes quotients of three-dimensional complex tori by finite groups acting freely in codimension one or two, using orbifold Chern classes and introducing new notions applicable to complex spaces with singularities.

## Contribution

It introduces a novel characterization of such quotients via orbifold Chern classes and extends the theory to complex spaces with klt singularities.

## Key findings

- Characterization of quotients via vanishing orbifold Chern classes
- Introduction of the 'birational' second Chern class for singular spaces
- Discussion of relations to Schwartz-MacPherson Chern classes

## Abstract

We provide a characterization of quotients of three-dimensional complex tori by finite groups that act freely in codimension one via a vanishing condition on the first and second orbifold Chern class. We also treat the case of actions free in codimension two, using instead the "birational" second Chern class, as we call it. Both notions of Chern classes are introduced here in the setting of compact complex spaces with klt singularities. In such generality, this topic has not been treated in the literature up to now. We also discuss the relation of our definitions to the classical Schwartz-MacPherson Chern classes.