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arXiv · 0704.0661

Ample subvarieties and rationally connected fibrations

Mauro C. Beltrametti·Tommaso de Fernex·Antonio Lanteri
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Abstract

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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Mauro C. Beltrametti, Tommaso de Fernex, Antonio Lanteri. 2008-03-05. Ample subvarieties and rationally connected fibrations. https://arxiv.org/abs/0704.0661

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