On Fano manifolds of large index (Q802685)

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.