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arXiv · 1601.07299

Flag bundles on Fano manifolds

Gianluca Occhetta·Luis E. Solá Conde·Jarosław A. Wiśniewski
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Abstract

As an application of a recent characterization of complete flag manifolds as Fano manifolds having only ${\mathbb P}^1$-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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BibTeXRIS

Gianluca Occhetta, Luis E. Solá Conde, Jarosław A. Wiśniewski. 2016-01-27. Flag bundles on Fano manifolds. https://arxiv.org/abs/1601.07299

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