Positivity of the canonical bundle and Hermitian metrics with quasi-negative holomorphic sectional curvature
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Wan, Xueyuan
Institution: Chongqing University of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220967121