In this paper we study smooth complex projective polarized varieties (X,H) of dimension n ge 2 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.
Rationally cubic connected manifolds I: manifolds covered by lines / Occhetta, Gianluca; Paterno, Valentina. - In: JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN. - ISSN 0025-5645. - STAMPA. - 64:3(2012), pp. 941-967. [10.2969/jmsj/06430941]
Rationally cubic connected manifolds I: manifolds covered by lines
Occhetta, Gianluca;Paterno, Valentina
2012-01-01
Abstract
In this paper we study smooth complex projective polarized varieties (X,H) of dimension n ge 2 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.File | Dimensione | Formato | |
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