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.
Original language | English (US) |
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Pages (from-to) | 573-579 |
Number of pages | 7 |
Journal | Journal of Differential Geometry |
Volume | 107 |
Issue number | 3 |
DOIs | |
State | Published - Nov 2017 |
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology