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

##### MSC:
 14J45 Fano varieties 14M20 Rational and unirational varieties
##### Keywords:
rational connectivity; Fano variety
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##### References:
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