Rationally cubic connected manifolds I: manifolds covered by lines

Gianluca Occhetta; Valentina Paterno

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arXiv · 1003.4936

Rationally cubic connected manifolds I: manifolds covered by lines

Gianluca Occhetta·Valentina Paterno

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Abstract

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.

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Gianluca Occhetta, Valentina Paterno. 2010-03-25. Rationally cubic connected manifolds I: manifolds covered by lines. https://arxiv.org/abs/1003.4936

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