Under some positivity assumptions, estension properties of rationally connected fibrations from a submanifold to its ambient variety are studied. Given a family of rational curves on a complex projective manifolds X inducing a covering family on a submanifold Y with ample normal bundle in X, the main results relate, under suitable conditions, the associated rational connected fiber structures on X and on Y. Applications of these results include an extension theorem for Mori contractions of fiber type and a classification theorem in the case Y has a structure of projective bundle or quadric fibration.
Ample subvarieties and rationally connected fibrations / M.C. Beltrametti, T. de Fernex, A. Lanteri. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 341:4(2008 Aug), pp. 897-926.
Ample subvarieties and rationally connected fibrations
A. LanteriUltimo
2008
Abstract
Under some positivity assumptions, estension properties of rationally connected fibrations from a submanifold to its ambient variety are studied. Given a family of rational curves on a complex projective manifolds X inducing a covering family on a submanifold Y with ample normal bundle in X, the main results relate, under suitable conditions, the associated rational connected fiber structures on X and on Y. Applications of these results include an extension theorem for Mori contractions of fiber type and a classification theorem in the case Y has a structure of projective bundle or quadric fibration.Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.