2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72996Here we introduce the concept of special effect curve which permits to study, from a different point of view, special linear systems in P^2, i.e. linear system with general multiple base points whose effective dimension is strictly greater than the expected one. In particular we study two different kinds of special effect: the α-special effect is defined by requiring some numerical conditions, while the definition of h^1-special effect concerns cohomology groups. We state two new conjectures for the characterization of special linear systems and we prove they are equivalent to the Segre and the Harbourne-Hirschowitz ones.LATEX, 15 pagesAlgebraic Geometry14C20 (Primary). 14N05, 14H20, 41A05 (Secondary)text