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On Fano manifolds of large index. (English) Zbl 0726.14028
This paper is a continuation of the author’s investigation about the characterization of Fano manifolds [ibid. 68, No.2, 135-141 (1990; Zbl 0715.14033)], where Fano manifolds X with $$n\leq 2r-2$$ were studied where $$n=\dim (X)$$ and r its index.
In this note, Fano manifolds with $$n=2r-1$$ are studied. The author shows that for such manifolds their Picard numbers is equal to 1 except in 3 cases. - The main tool of this paper is to use an idea of Mori to construct a family of deformations of a rational curve on X.

##### MSC:
 14J45 Fano varieties 14C22 Picard groups
##### Keywords:
large index; Fano manifolds; Picard numbers
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##### References:
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