Special systems through double points on an algebraic surface

Original · EN

Let S be a smooth algebraic surface satisfying the following property: Hⁱ(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.