Year: 2026
Type: preprint
Abstract: Let $f\colon X\toΔ$ be a smooth Kähler morphism from complex manifold $X$ to the unit disc. We prove that the canonical bundle $K_{X_t}$ is nef for \emph{every} fiber as soon as it is nef for \emph{one} fiber. This answers, in arbitrary dimension and in the Kähler setting, the deformation-openness problem for non-nefness of the canonical bundle raised by Campana and Peternell.
Source: arXiv (Cornell University)
Authors: Li, Mu-Lin, Liu, Xiao-Lei, Rao, Sheng
Institution: Hunan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1563298894, G3414394961, G500947340
OpenAlex ID: W7213238558