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Zbl 0783.14022
Campana, F.
Rational connectivity of Fano varieties. (Connexité rationnelle des variétés de Fano.) (French)
[J] Ann. Sci. Éc. Norm. Supér. (4) 25, No. 5, 539-545 (1992). ISSN 0012-9593

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

MSC 2000:: *14J45 Fano varieties
14M20 Rational varieties

Keywords: rational connectivity; Fano variety

Citations: Zbl 0759.14032

Cited in: Zbl 1093.14059 Zbl 1081.14060 Zbl 0939.14008 Zbl 0948.14014

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