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PreprintarXiv licencearXiv

Positivity of the canonical bundle and Hermitian metrics with quasi-negative holomorphic sectional curvature

  • Xueyuan Wan
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Abstract

We prove that if a compact Kähler manifold admits a Hermitian metric with quasi-negative holomorphic sectional curvature for the Chern connection, then its canonical bundle is ample. The Hermitian metric realizing this curvature need not be Kähler. This proves the Kähler case of the quasi-negative conjecture of Yang and Zheng.

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Cite

BibTeXRIS
BibTeX
@misc{wan2026positivity,
  title = {{Positivity of the canonical bundle and Hermitian metrics with quasi-negative holomorphic sectional curvature}},
  author = {Xueyuan Wan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08111},
  eprint = {2610.08111},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08111},
}
RIS
TY  - UNPB
TI  - Positivity of the canonical bundle and Hermitian metrics with quasi-negative holomorphic sectional curvature
AU  - Xueyuan Wan
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08111
UR  - https://arxiv.org/abs/2610.08111
AB  - We prove that if a compact Kähler manifold admits a Hermitian metric with quasi-negative holomorphic sectional curvature for the Chern connection, then its canonical bundle is ample. The Hermitian metric realizing this curvature need not be Kähler. This proves the Kähler case of the quasi-negative conjecture of Yang and Zheng.
ER  -