Ample vector bundles with sections vanishing on submanifolds of sectional genus three

摘要

Let be an ample vector bundle of rank r > 2 on a smooth complex projective variety X of dimension n such that there exists a global section of whose zero locus Z is a smooth subvariety of dimension n - r > 2 of X Let H be an ample line bundle on X such that H defines an embedding of Z. The triplets (X,H) with g(Z,Hz) = 3 aie classified, where g{Z,Hz) is the sectional genus of (Z,Hz) This is the first step towards the classification of the ample vector bundles of rank n - 1 on X of curve genus three.