Geometrically ruled surfaces as zero loci of ample vector bundles

Let E be an ample vector bundle of rank n-2 on a complex projective manifold X of dimension n, having a section whose zero locus is a smooth surface Z. Pairs (X,E) as above are classified under the assumption that Z is a P^1-bundle over a smooth curve. We also prove that X has negative Kodaira dimension if, in a similar setting, Z is a birationally ruled surface.