6
$\begingroup$

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.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
6
$\begingroup$

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.

enter image description here

Improve this answer
$\endgroup$
3
  • $\begingroup$ Thank you, but the problem that It is not available on the internet Do you have a pdf version $\endgroup$
    – Kamel
    Commented Aug 1, 2020 at 21:44
  • 2
    $\begingroup$ 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 $\endgroup$
    – Francesco Polizzi
    Commented Aug 1, 2020 at 21:48
  • $\begingroup$ Okay, thank you so much $\endgroup$
    – Kamel
    Commented Aug 1, 2020 at 22:05

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .