Year: 2026
Type: preprint
Abstract: We study the deformation stability of Kähler and balanced hyperbolicity. We prove that Kähler hyperbolicity is open under arbitrary small holomorphic deformations, but need not be closed, even in families of smooth projective surfaces. By contrast, balanced hyperbolicity is not open in general: in every complex dimension at least five, we construct a balanced hyperbolic central fibre with non-balanced nearby fibres. We establish criteria for the deformation stability of balanced hyperbolicity using Aeppli cohomology and Lefschetz theory. For principal holomorphic torus bundles over products of curves of genus at least two, we compute the relevant hyperbolic cohomology, obtain a numerical characterization of balanced hyperbolicity, and prove its openness under small deformations.
Source: arXiv (Cornell University)
Authors: Fu, Jixiang, Wu, Jingcao
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G8029918014
OpenAlex ID: W7211880564