A classification theorem on Fano bundles  [ Un théoréme de classification sur les fibrés de Fano ]
Annales de l'Institut Fourier, Tome 64 (2014) no. 1, p. 341-373
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.
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.
DOI : https://doi.org/10.5802/aif.2850
Classification:  14M15,  14E30,  14J45
Mots clés: fibrés vectorielles, variétés de Fano
@article{AIF_2014__64_1_341_0,
     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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {1},
     year = {2014},
     pages = {341-373},
     doi = {10.5802/aif.2850},
     zbl = {1317.14108},
     mrnumber = {3330489},
     zbl = {06387277},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_1_341_0}
}
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. http://www.numdam.org/item/AIF_2014__64_1_341_0/

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