English

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.

Keywords

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}
}
R2 v1 2026-06-22T09:38:55.541Z