Ample vector bundles with zero loci of small Δ-genera

Abstract Let X be a smooth complex projective variety endowed with an ample vector bundle ε admitting a global section whose zero locus is a smooth subvariety Z of the expected dimension, and let H be an ample line bundle on X, whose restriction HZ to Z is very ample. Triplets (X, ε, H) are studied and classified under the assumption that the delta genus of (Z, HZ ) is either small (≤ 3) or small in comparison with the corank of ε or the degree.