# Mori's cone theorem

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.

## 1 Answer

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.

• Thank you, but the problem that It is not available on the internet Do you have a pdf version – Kamel Aug 1 at 21:44
• I have a paper copy. At any rate, you can find the same result in these GAEL notes by Debarre: math.ens.fr/~debarre/NotesGAEL.pdf – Francesco Polizzi Aug 1 at 21:48
• Okay, thank you so much – Kamel Aug 1 at 22:05