We study smooth complex projective polarized varieties of dimension which admit a dominating family of rational curves of -degree , such that two general points of may be joined by a curve parametrized by and which do not admit a covering family of lines (i.e., rational curves of -degree one). We prove that such manifolds are obtained from RCC manifolds of Picard number one by blow-ups along smooth centers. If we further assume that is a Fano manifold, we obtain a stronger result, classifying all Fano RCC manifolds of Picard number .
Cite this article
Gianluca Occhetta, Valentina Paterno, Rationally cubic connected manifolds II. Rev. Mat. Iberoam. 28 (2012), no. 3, pp. 815–838DOI 10.4171/RMI/692