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.
Rationally cubic connected manifolds II
Occhetta, Gianluca;Paterno, Valentina
2012-01-01
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
