A classification theorem on Fano bundles
Annales de l'Institut Fourier, Volume 64 (2014) no. 1, pp. 341-373.

In this paper we classify rank two Fano bundles on Fano manifolds satisfying H 2 (X,)H 4 (X,). The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization (), that allows us to obtain the cohomological invariants of X and . As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.

Dans cet article, on classifie les fibrés de Fano de rang deux sur les variétés de Fano satisfaisant H 2 (X,)H 4 (X,). La classification est obtenue par le calcul des cônes nef et pseudoeffectif de la projectivation (), ce qui nous permet d’obtenir des invariants cohomologiques de X et . Comme un sous-produit, nous discutons des fibrés associés à Fano congruences de droites, montrant que leurs variétés de tangentes rationnelles minimales peuvent avoir plusieurs composants linéaires.

DOI: 10.5802/aif.2850
Classification: 14M15, 14E30, 14J45
Keywords: vector bundles, Fano manifolds
Mot clés : fibrés vectorielles, variétés de Fano
Muñoz, Roberto 1; Solá Conde, Luis E. 1; Occhetta, Gianluca 2

1 ESCET Departamento de Matemática Aplicada Universidad Rey Juan Carlos Campus de Móstoles C/Tulipan S/N, 28933 Móstoles Madrid (Espagne)
2 Università di Trento Dipartimento di Matematica Via Sommarive 14, I-38123 Povo (TN), (Italie)
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Muñoz, Roberto; Solá Conde, Luis E.; Occhetta, Gianluca. A classification theorem on Fano bundles. Annales de l'Institut Fourier, Volume 64 (2014) no. 1, pp. 341-373. doi : 10.5802/aif.2850. http://archive.numdam.org/articles/10.5802/aif.2850/

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