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arXiv · 2609.14435

Deformation invariance of canonical nefness in smooth Kahler morphisms

Mu-Lin Li·Xiao-Lei Liu·Sheng Rao
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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.

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Mu-Lin Li, Xiao-Lei Liu, Sheng Rao. 2026-09-13. Deformation invariance of canonical nefness in smooth Kahler morphisms. https://arxiv.org/abs/2609.14435

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