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PreprintCC BY 4.0arXiv

Deformation invariance of canonical nefness in smooth Kahler morphisms

  • Mu-Lin Li
  • Xiao-Lei Liu
  • Sheng Rao
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Abstract

Let f: X→Δ be a smooth Kähler morphism from complex manifold X to the unit disc. We prove that the canonical bundle KXt 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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Cite

BibTeXRIS
BibTeX
@misc{li2026deformation,
  title = {{Deformation invariance of canonical nefness in smooth Kahler morphisms}},
  author = {Mu-Lin Li and Xiao-Lei Liu and Sheng Rao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14435},
  eprint = {2609.14435},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14435},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Deformation invariance of canonical nefness in smooth Kahler morphisms
AU  - Mu-Lin Li
AU  - Xiao-Lei Liu
AU  - Sheng Rao
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14435
UR  - https://arxiv.org/abs/2609.14435
AB  - Let f: X→Δ 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.
ER  -