A classification theorem on Fano bundles

Muñoz, Roberto; Solá Conde, Luis E.; Occhetta, Gianluca

doi:10.5802/aif.2850

A classification theorem on Fano bundles
[Un théoréme de classification sur les fibrés 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)

Annales de l'Institut Fourier, Tome 64 (2014) no. 1, pp. 341-373.

Résumé
Abstract

Dans cet article, on classifie les fibrés de Fano de rang deux $ℰ$ sur les variétés de Fano satisfaisant $H^{2} (X, ℤ) ≅ H^{4} (X, ℤ) ≅ ℤ$ . La classification est obtenue par le calcul des cônes nef et pseudoeffectif de la projectivation $ℙ (ℰ)$ , ce qui nous permet d’obtenir des invariants cohomologiques de $X$ et $ℰ$ . 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.

In this paper we classify rank two Fano bundles $ℰ$ on Fano manifolds satisfying $H^{2} (X, ℤ) ≅ H^{4} (X, ℤ) ≅ ℤ$ . The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization $ℙ (ℰ)$ , that allows us to obtain the cohomological invariants of $X$ and $ℰ$ . 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.

EuDML MR Zbl

DOI : 10.5802/aif.2850

Classification : 14M15, 14E30, 14J45
Keywords: vector bundles, Fano manifolds
Mot clés : fibrés vectorielles, variétés de Fano

Affiliations des auteurs :

Muñoz, Roberto ¹ ; Solá Conde, Luis E. ¹ ; Occhetta, Gianluca ²

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     author = {Mu\~noz, Roberto and Sol\'a Conde, Luis E. and Occhetta, Gianluca},
     title = {A classification theorem on {Fano} bundles},
     journal = {Annales de l'Institut Fourier},
     pages = {341--373},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {64},
     number = {1},
     year = {2014},
     doi = {10.5802/aif.2850},
     zbl = {1317.14108},
     mrnumber = {3330489},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2850/}
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Muñoz, Roberto; Solá Conde, Luis E.; Occhetta, Gianluca. A classification theorem on Fano bundles. Annales de l'Institut Fourier, Tome 64 (2014) no. 1, pp. 341-373. doi : 10.5802/aif.2850. https://aif.centre-mersenne.org/articles/10.5802/aif.2850/

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