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.
Ample subvarieties and rationally connected fibrations
BELTRAMETTI, MAURO CARLO;
2008-01-01
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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