A note on the classification of Fano manifolds of middle index
In the classification of Fano manifolds of middle index, that is manifolds \(X\) of index \(r\) and \(\dim X = 2r\), the case of a Fano manifold of dimension \(6\), index \(3\) and Picard number two whose extremal contractions are \({\mathbb P}^{2}\)-bundles was a doubtful case. In the paper under review the author rules out such a case by studying unsplit families of rational curves. See [\textit{J. A. Wiśniewski} in: Projective geometry with applications, Lect. Notes Pure Appl. Math. 166, 19--26 (1994; Zbl 0839.14032)] for an account on Fano manifolds of middle index and \(b_{2}\geq 2\).
scientific article; zbMATH DE number 2175527