A complex analytic approach to orbifold Chern classes on singular varieties and its applications
Abstract
In this article, we prove the orbifold version of the Bogomolov-Gieseker inequality for stable $\mathbb Q$-sheaves on Kähler varieties, generalizing our earlier work \cite{GP25} in dimension three. We also provide a characterization of the equality case, a new purely analytical proof of the numerical characterization of complex torus quotients as well as a novel, complex analytic interpretation of the second orbifold Chern class associated to a $\mathbb Q$-sheaf.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Geometry and complex manifolds
Algebraic structures and combinatorial models
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 January 2026
- Language
- EN
- Document type
- Preprint