On ratios of Chern numbers for complex hyperbolic branched covers
Abstract
In this paper we prove that, at least in even complex dimensions, the ratio of Chern numbers for a closed complex hyperbolic branched cover manifold are not all equal to the corresponding ratio of Chern numbers for a closed complex hyperbolic manifold. This leads to an answer for a question posed by Deraux and Seshadri [Proc. Amer. Math. Soc. 139 (2011), pp. 2571–2576], and proves that an almost 1 / 4 1/4 -pinched metric constructed by the author in a previous article is not Kähler.
Fields of Study & Subjects
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Geometric and Algebraic Topology
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 8
- Pages
- 3583–3591
- Publication date
- 5 March 2026
- Language
- EN