Finite quotients of three-dimensional complex tori

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.

v1: preliminary version, the case of actions free in codimension two; v2: significantly expanded version, new features: generalization to actions free in codimension one and discussion of orbifold Chern classes

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• Groups with exotic finiteness properties from complex Morse theory