2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112652Let S be a smooth algebraic surface satisfying the following property: H^i(\oc_S(C))=0 (i=1,2) for any irreducible and reduced curve C 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 general position. As an application, the dimension of such systems is evaluated in case S is an Abelian, an Enriques, a K3 or an anticanonical rational surface.10 pages, LaTeXAlgebraic Geometry14C20text