%0 Journal Article
%T Rationally cubic connected manifolds I: manifolds covered by lines
%A Gianluca Occhetta
%A Valentina Paterno
%J Mathematics
%D 2010
%I arXiv
%X In this paper we study smooth complex projective polarized varieties (X,H) of dimension n \ge 2 which admit a dominating family V of rational curves of H-degree 3, such that two general points of X may be joined by a curve parametrized by V, and such that there is a covering family of rational curves of H-degree one. Our main result is that the Picard number of these manifolds is at most three, and that, if equality holds, (X,H) has an adjuction theoretic scroll structure over a smooth variety.
%U http://arxiv.org/abs/1003.4936v1