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EnglishWe 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.
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| Titolo: | Rationally cubic connected manifolds II |
| Autori Unitn: | Occhetta, Gianluca Paterno, Valentina |
| Anno di pubblicazione: | 2012 |
| Titolo del periodico: | REVISTA MATEMATICA IBEROAMERICANA |
| 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. |
| Handle: | http://hdl.handle.net/11572/90597 |
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