An extension of a theorem of Wu-Yau

Abstract

We show that a compact Kahler 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.

6 pages; final version to appear in J. Differential Geom

References in corpus (1)

• Negative Holomorphic curvature and positive canonical bundle

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• Reduction of manifolds with semi-negative holomorphic sectional curvature
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• A remark on our paper "Negative Holomorphic curvature and positive canonical bundle"
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• Vanishing theorems and rational connectedness on holomorphic tensor fields
• The Wu-Yau theorem on Sasakian manifolds
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