An extension of a theorem of Wu-Yau

Valentino Tosatti, Xiaokui Yang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)573-579
Number of pages7
JournalJournal of Differential Geometry
Issue number3
StatePublished - Nov 2017

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


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