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arXiv · 1009.3811

Rationally cubic connected manifolds II

Gianluca Occhetta·Valentina Paterno
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Abstract

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 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 $ρ_X \ge 3$

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Gianluca Occhetta, Valentina Paterno. 2010-09-20. Rationally cubic connected manifolds II. https://arxiv.org/abs/1009.3811

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