Rational connectivity of Fano varieties. (Connexité rationnelle des variétés de Fano.) (French) Zbl 0783.14022

Campana, F.

Ann. Sci. Éc. Norm. Supér. (4) 25, No. 5, 539-545 (1992).

It is shown that a Fano variety \(X\), i.e., a nonsingular projective variety with \(-K_ X\) ample, is rationally connected. Namely, for any two points \(x,y\) of \(X\) there is a connected chain of rational curves \(C=\bigcup_{1 \leq i \leq n}C_ i\) such that \(x\), \(y \in C\). This result was also proved by J. Kollar, Y. Miyaoka and S. Mori [J. Differ. Geom. 36, No. 3, 765-779 (1992; Zbl 0759.14032)].

Reviewer: M.Miyanishi (Toyonaka / Osaka)

MSC:

14J45	Fano varieties
14M20	Rational and unirational varieties

Keywords:

rational connectivity; Fano variety

Citations:

Zbl 0759.14032

References:

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