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Numerical characterization of complex torus quotients

Abstract : 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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Contributor : Henri Guenancia Connect in order to contact the contributor
Submitted on : Wednesday, July 20, 2022 - 6:13:36 PM
Last modification on : Tuesday, August 2, 2022 - 11:34:41 AM


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  • HAL Id : hal-03344158, version 2


Benoît Claudon, Patrick Graf, Henri Guenancia. Numerical characterization of complex torus quotients. Commentarii Mathematici Helvetici, European Mathematical Society, In press. ⟨hal-03344158v2⟩



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