Ample vector bundles with zero loci of sectional genus two

Let X be a smooth complex projective variety and let be a smooth submanifold of dimension , which is the zero locus of a section of an ample vector bundle of rank on X. Let H be an ample line bundle on X, whose restriction H_Z to Z is generated by global sections. Triplets as above are classified under the assumption that is a polarized manifold of sectional genus 2. This can be regarded as a step towards the classification of ample vector bundles of corank one and curve genus two. Received: 6 June 2003