Let \mathscr{E} be an ample vector bundle of rank r on a smooth complex projective manifold X of dimension n≥r+3. Pairs (X, \mathscr{E}) as above are investigated under the assumption that \mathscr{E} has a regular section vanishing along a Fano manifold Z of index dim Z−1 and Picard number ρ(Z)≥2.
