# Rationally cubic connected manifolds II

### Gianluca Occhetta

Università di Trento, Povo (Trento), Italy### Valentina Paterno

Università di Trento, Povo (Trento), Italy

## Abstract

We study smooth complex projective polarized varieties $(X,H)$ of dimension $n≥2$ 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 which do not admit a covering family of lines (i.e., rational curves of $H$-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 $X$ is a Fano manifold, we obtain a stronger result, classifying all Fano RCC manifolds of Picard number $ρ_{X}≥3$.

## Cite this article

Gianluca Occhetta, Valentina Paterno, Rationally cubic connected manifolds II. Rev. Mat. Iberoam. 28 (2012), no. 3, pp. 815–838

DOI 10.4171/RMI/692