As an application of a recent characterization of complete flag manifolds as Fano manifolds having only P1-bundles as elementary contractions, we consider here the case of a Fano manifold X of Picard number one supporting an unsplit family of rational curves whose subfamilies parametrizing curves through a fixed point are rational homogeneous, and we prove that X is homogeneous. In order to do this, we first study minimal sections on flag bundles over the projective line, and discuss how Grothendieck's theorem on principal bundles allows us to describe a flag bundle upon some special sections.

Flag bundles on Fano manifolds / Occhetta, Gianluca; Sola Conde, Eduardo Luis; Wiśniewski, Jarosław A.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 2016, volume 106:4(2016), pp. 651-669. [10.1016/j.matpur.2016.03.006]

Flag bundles on Fano manifolds

Occhetta, Gianluca;Sola Conde, Eduardo Luis;
2016

Abstract

As an application of a recent characterization of complete flag manifolds as Fano manifolds having only P1-bundles as elementary contractions, we consider here the case of a Fano manifold X of Picard number one supporting an unsplit family of rational curves whose subfamilies parametrizing curves through a fixed point are rational homogeneous, and we prove that X is homogeneous. In order to do this, we first study minimal sections on flag bundles over the projective line, and discuss how Grothendieck's theorem on principal bundles allows us to describe a flag bundle upon some special sections.
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Occhetta, Gianluca; Sola Conde, Eduardo Luis; Wiśniewski, Jarosław A.
Flag bundles on Fano manifolds / Occhetta, Gianluca; Sola Conde, Eduardo Luis; Wiśniewski, Jarosław A.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 2016, volume 106:4(2016), pp. 651-669. [10.1016/j.matpur.2016.03.006]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/142979
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