c © 1998 Universitat de Barcelona Ample vector bundles with sections vanishing along conic fibrations over curves

LetE be an ample vector bundle of rank r ≥ 2 on a complex projective manifold X of dimensionn = r+2 having a section whose zero locus is a smooth surface Z. Pairs (X, E) as above are classified under the assumption that (Z,LZ) is a conic fibration over a smooth curve for some ample line bundle L on X. In the last 20 years the study of special varieties as ample divisors attracted the attention of many authors. This subject grows up from the classical studies con-cerning hyperplane sections. Recently Lanteri and Maeda reconsidered this theme looking at smooth subma