Numerical characterization of complex torus quotients
Benoît ClaudonUniversité de Rennes I, CNRS; Institut Universitaire de France, Rennes, France
Patrick GrafUniversität Bayreuth, Germany
Henri GuenanciaUniversité Paul Sabatier, Toulouse, France
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.
Cite this article
Benoît Claudon, Patrick Graf, Henri Guenancia, Numerical characterization of complex torus quotients. Comment. Math. Helv. 97 (2022), no. 4, pp. 769–799DOI 10.4171/CMH/543