A classification theorem on Fano bundles

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.