Journal of Differential Geometry
- J. Differential Geom.
- Volume 107, Number 3 (2017), 573-579.
An extension of a theorem of Wu–Yau
We show that a compact Kähler 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.
The first author was supported in part by a Sloan Research Fellowship and NSF grant DMS-1308988.
The second author was supported in part by China’s Recruitment Program of Global Experts and by Hua Loo-Keng Center for Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
J. Differential Geom., Volume 107, Number 3 (2017), 573-579.
Received: 26 November 2015
First available in Project Euclid: 21 October 2017
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Tosatti, Valentino; Yang, Xiaokui. An extension of a theorem of Wu–Yau. J. Differential Geom. 107 (2017), no. 3, 573--579. doi:10.4310/jdg/1508551226. https://projecteuclid.org/euclid.jdg/1508551226