TITLE: Mori's cone theorem
QUESTION [6 upvotes]: I need the proof (reference) of Mori’s theorem about this implication :
Let  $X$ be a projective complex manifold. If $X$ contains no rational curves, then $K_K$ is nef.

REPLY [6 votes]: A more precise form of this result is originally due to Miyaoka and Mori, see Theorem 3.6 page 67 in
Olivier Debarre: Higher-dimensional algebraic geometry, Universitext. New York, NY: Springer. xiii, 233 p. (2001). ZBL0978.14001.