Negative Holomorphic curvature and positive canonical bundle
Differential Geometry
2016-05-04 v1 Algebraic Geometry
Abstract
In this note we show that if a projective manifold admits a K\"ahler metric with negative holomorphic sectional curvature then the canonical bundle of the manifold is ample. This confirms a conjecture of the second author.
Cite
@article{arxiv.1505.05802,
title = {Negative Holomorphic curvature and positive canonical bundle},
author = {Damin Wu and Shing-Tung Yau},
journal= {arXiv preprint arXiv:1505.05802},
year = {2016}
}