Journal of Differential Geometry

An extension of a theorem of Wu–Yau

Valentino Tosatti and Xiaokui Yang

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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.

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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.

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