CLASSIFICATION OF RANK-2 AMPLE AND SPANNED VECTOR-BUNDLES ON SURFACES WHOSE ZERO LOCI CONSIST OF GENERAL POINTS

Let X be an n-dimensional smooth projective variety over an algebraically closed field k of characteristic zero, and E an ample and spanned vector bundle of rank n on X. To study the geometry of (X, E) in view of the zero loci of global sections of E, Ballico introduces a numerical invariant s(E). The purposes of this paper are to give a cohomological interpretation of s(E), and to classify ample and spanned rank-2 bundles E on smooth complex surfaces X with s(E) = 2c2(E), or 2c2(E) - 1 ; namely ample and spanned 2-bundles whose zero loci of global sections consist of general c2 (E) points or general c2(E) - 1 points plus one. As an application of these classification, we classify rank-2 ample and spanned vector bundles E on smooth complex projective surfaces with c2(E) = 2.