Open Access
November 2017 An extension of a theorem of Wu–Yau
Valentino Tosatti, Xiaokui Yang
Author Affiliations +
J. Differential Geom. 107(3): 573-579 (November 2017). DOI: 10.4310/jdg/1508551226


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.

Funding Statement

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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Valentino Tosatti. Xiaokui Yang. "An extension of a theorem of Wu–Yau." J. Differential Geom. 107 (3) 573 - 579, November 2017.


Received: 26 November 2015; Published: November 2017
First available in Project Euclid: 21 October 2017

zbMATH: 06846972
MathSciNet: MR3715350
Digital Object Identifier: 10.4310/jdg/1508551226

Rights: Copyright © 2017 Lehigh University

Vol.107 • No. 3 • November 2017
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