Abstract
In this paper we study smooth complex projective polarized varieties (X,H) of dimension n ≥ 2 which admit a covering family V of rational curves of degree 3 with respect to H 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.
We prove that the Picard number of these manifolds is at most three, and that, if equality holds, (X,H) has an adjunction theoretic scroll structure over a smooth variety.
Citation
Gianluca OCCHETTA. Valentina PATERNO. "Rationally cubic connected manifolds I: manifolds covered by lines." J. Math. Soc. Japan 64 (3) 941 - 967, July, 2012. https://doi.org/10.2969/jmsj/06430941
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