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arXiv · 2610.08111

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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Xueyuan Wan. 2026-10-06. Positivity of the canonical bundle and Hermitian metrics with quasi-negative holomorphic sectional curvature. https://arxiv.org/abs/2610.08111

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