An extension of a theorem of Wu-Yau
classification
🧮 math.DG
math.AG
keywords
bundlecanonicalconjecturecurvatureholomorphicsectionalwu-yauample
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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.
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