A classification theorem on Fano bundles

[Un théoréme de classification sur les fibrés de Fano]

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

Annales de l'Institut Fourier, Tome 64 (2014), p. 341-373 / Harvested from Numdam

Résumé

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

Abstract

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

Détail

Publié le : 2014-01-01

MR 3330489 | Zbl 06387277 | Zbl 1317.14108

DOI : https://doi.org/10.5802/aif.2850
Classification:  14M15,  14E30,  14J45
Mots clés: fibrés vectorielles, variétés de Fano

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