Ample subvarieties and rationally connected fibrations
Algebraic Geometry
2008-03-05 v3
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.
Keywords
Cite
@article{arxiv.0704.0661,
title = {Ample subvarieties and rationally connected fibrations},
author = {Mauro C. Beltrametti and Tommaso de Fernex and Antonio Lanteri},
journal= {arXiv preprint arXiv:0704.0661},
year = {2008}
}
Comments
27 pages; v2: minor changes and corrections following the referee's comments. v3: few typos corrected. To appear in Math. Ann