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.
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.
Citation
Valentino Tosatti. Xiaokui Yang. "An extension of a theorem of Wu–Yau." J. Differential Geom. 107 (3) 573 - 579, November 2017. https://doi.org/10.4310/jdg/1508551226
