On Fano manifolds of large index.

*(English)*Zbl 0726.14028This 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.

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.

Reviewer: Vo Van Tan (Boston)

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