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