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arXiv · 2109.06738

Numerical characterization of complex torus quotients

Benoît Claudon·Patrick Graf·Henri Guenancia
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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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BibTeXRIS

Benoît Claudon, Patrick Graf, Henri Guenancia. 2021-09-14. Numerical characterization of complex torus quotients. https://doi.org/10.4171/cmh%2F543

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