Surface

Abstract

. Let S be a smooth projective algebraic surface satisfying the following property: H i ( S,B ) = 0 for i > 0, for any irreducible and reduced curve B of S . The aim of this paper is to provide a characterization of special linear systems on S which are singular along a set of double points in very general position. As an application, the dimension of such systems is evaluated in case S is a simple Abelian surface, a K 3 surface which does not contain elliptic curves or an anticanonical rational surface.