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Ample subvarieties and rationally connected fibrations

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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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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146, Genova, Italy

    Mauro C. Beltrametti

  2. Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT, 84112, USA

    Tommaso de Fernex

  3. Dipartimento di Matematica “F. Enriques”, Università di Milano, Via C. Saldini 50, 20133, Milano, Italy

    Antonio Lanteri

Authors
  1. Mauro C. Beltrametti
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  2. Tommaso de Fernex
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  3. Antonio Lanteri
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Corresponding author

Correspondence to Mauro C. Beltrametti.

Additional information

All authors acknowledge support by MIUR National Research Project “Geometry on Algebraic Varieties” (Cofin 2004). The research of the second author was partially supported by NSF grants DMS 0111298 and DMS 0548325. The third author acknowledges partial support by the University of Milan (FIRST 2003).

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Beltrametti, M.C., de Fernex, T. & Lanteri, A. Ample subvarieties and rationally connected fibrations. Math. Ann. 341, 897–926 (2008). https://doi.org/10.1007/s00208-008-0217-4

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  • DOI: https://doi.org/10.1007/s00208-008-0217-4

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