A Fano manifold X with nef tangent bundle is of Flag-Type if it has the same kind of elementary contractions as a complete flag manifold. In this paper we present a method to associate a Dynkin diagram D(X) with any such X, based on the numerical properties of its contractions. We then show that D(X) is the Dynkin diagram of a semisimple Lie group. As an application we prove that Campana–Peternell conjecture holds when X is a Flag-Type manifold whose Dynkin diagram is An, i.e. we show that X is the variety of complete flags of linear subspaces in Pn.

Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle / Muñoz, Roberto; Occhetta, Gianluca; Sola Conde, Eduardo Luis; Watanabe, Kiwamu. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - STAMPA. - 361:3-4(2015), pp. 583-609. [10.1007/s00208-014-1083-x]

Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle

Occhetta, Gianluca;Sola Conde, Eduardo Luis;
2015-01-01

Abstract

A Fano manifold X with nef tangent bundle is of Flag-Type if it has the same kind of elementary contractions as a complete flag manifold. In this paper we present a method to associate a Dynkin diagram D(X) with any such X, based on the numerical properties of its contractions. We then show that D(X) is the Dynkin diagram of a semisimple Lie group. As an application we prove that Campana–Peternell conjecture holds when X is a Flag-Type manifold whose Dynkin diagram is An, i.e. we show that X is the variety of complete flags of linear subspaces in Pn.
2015
3-4
Muñoz, Roberto; Occhetta, Gianluca; Sola Conde, Eduardo Luis; Watanabe, Kiwamu
Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle / Muñoz, Roberto; Occhetta, Gianluca; Sola Conde, Eduardo Luis; Watanabe, Kiwamu. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - STAMPA. - 361:3-4(2015), pp. 583-609. [10.1007/s00208-014-1083-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/104661
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