English

An extension of a theorem of Wu-Yau

Differential Geometry 2017-10-24 v3 Algebraic Geometry

Abstract

We show that a compact Kahler manifold with nonpositive holomorphic sectional curvature has nef canonical bundle. If the holomorphic sectional curvature is negative then it follows that the canonical bundle is ample, confirming a conjecture of Yau. The key ingredient is the recent solution of this conjecture in the projective case by Wu-Yau.

Keywords

Cite

@article{arxiv.1506.01145,
  title  = {An extension of a theorem of Wu-Yau},
  author = {Valentino Tosatti and Xiaokui Yang},
  journal= {arXiv preprint arXiv:1506.01145},
  year   = {2017}
}

Comments

6 pages; final version to appear in J. Differential Geom