Journal of Differential Geometry

An extension of a theorem of Wu–Yau

Valentino Tosatti and Xiaokui Yang

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Abstract

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.

Note

The first author was supported in part by a Sloan Research Fellowship and NSF grant DMS-1308988.

Note

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.

Article information

Source
J. Differential Geom., Volume 107, Number 3 (2017), 573-579.

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

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1508551226

Digital Object Identifier
doi:10.4310/jdg/1508551226

Mathematical Reviews number (MathSciNet)
MR3715350

Zentralblatt MATH identifier
06846972

Citation

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


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