Numerical characterization of complex torus quotients (Q2693161)

Summary: This article gives a characterization of quotients of complex tori by finite groups acting freely in codimension two in terms of a numerical vanishing condition on the first and second Chern class. This generalizes results previously obtained by Greb-Kebekus-Peternell in the projective setting, and by Kirschner and the second author in dimension three. As a key ingredient to the proof, we obtain a version of the Bogomolov-Gieseker inequality for stable sheaves on singular spaces, including a discussion of the case of equality.