Ample subvarieties and rationally connected fibrations

Details Ample subvarieties and rationally connected fibrations Ample subvarieties and rationally connected fibrations

2007-04-04

arxiv.org/abs/0704.0661v3

Mathematics

Algebraic Geometry

27 pages; v2: minor changes and corrections following the referee's comments. v3: few typos corrected. To appear in Math. Ann

Scientific paper

Under some positivity assumptions, extension properties of rationally connected fibrations from a submanifold to its ambient variety are studied. Given a family of rational curves on a complex projective manifold 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.

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