Numerical characterization of complex torus quotients
arXiv:2109.06738 · doi:10.4171/cmh/543
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.
arXiv comment26 pages, v2: exposition improved thanks to the referee's suggestions, added Proposition 3.5 in the semistable case, to appear in Comment. Math. Helv
References in corpus (9)
- Differential Forms on Log Canonical Spaces
- The global moduli theory of symplectic varieties
- A polarization identity for multilinear maps
- Fujiki relations and fibrations of irreducible symplectic varieties
- Kähler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups
- Fujiki relation on symplectic varieties
- A Donaldson-Uhlenbeck-Yau theorem for normal varieties and semistable bundles on degenerating families
- The Bogomolov's inequality on a singular complex space
- Variation of singular Kähler-Einstein metrics: Kodaira dimension zero