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Journal Articles Commentarii Mathematici Helvetici Year : 2022

Numerical characterization of complex torus quotients


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.
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Dates and versions

hal-03344158 , version 1 (14-09-2021)
hal-03344158 , version 2 (20-07-2022)



Benoît Claudon, Patrick Graf, Henri Guenancia. Numerical characterization of complex torus quotients. Commentarii Mathematici Helvetici, 2022, 97 (4), pp.769-799. ⟨10.4171/CMH/543⟩. ⟨hal-03344158v2⟩
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