In this paper we classify rank two Fano bundles $cE$ on Fano manifolds satisfying $H^2(X,Z)cong H^4(X,Z)congZ$. The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization $P(cE)$, that allows us to obtain the cohomological invariants of $X$ and $cE$. 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.
A classification theorem for Fano bundles / R., Muñoz; Occhetta, Gianluca; Sola Conde, Eduardo Luis. - In: ANNALES DE L'INSTITUT FOURIER. - ISSN 1777-5310. - STAMPA. - 64:1(2014), pp. 341-373. [10.5802/aif.2850]
A classification theorem for Fano bundles.
Occhetta, Gianluca;Sola Conde, Eduardo Luis
2014-01-01
Abstract
In this paper we classify rank two Fano bundles $cE$ on Fano manifolds satisfying $H^2(X,Z)cong H^4(X,Z)congZ$. The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization $P(cE)$, that allows us to obtain the cohomological invariants of $X$ and $cE$. 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.| File | Dimensione | Formato | |
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