On almost quasi-negative holomorphic sectional curvature
arXiv (Cornell University)(2020)
Abstract
A recent celebrated theorem of Diverio-Trapani and Wu-Yau states that a compact K\"ahler manifold admitting a K\"ahler metric of quasi-negative holomorphic sectional curvature has an ample canonical line bundle, confirming a conjecture of Yau. In this note we shall introduce a natural notion of \emph{almost quasi-negative holomorphic sectional curvature} and extend this theorem to compact K\"ahler manifolds of almost quasi-negative holomorphic sectional curvature. We also obtain a gap-type theorem for the inequality $\int_Xc_1(K_X)^n>0$ in terms of the holomorphic sectional curvature. The $\alpha$-invariant plays a key role in the discussions.
MoreTranslated text
Key words
quasi-negative
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined