2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61023In this paper, we examine Green and Lazarsfeld's Np property for rational surfaces obtained by blowing up the projective plane P^2 at a subscheme of fat points Z. We show that these surfaces, embedded into projective spaces by linear system of plane curves of degree t containing Z, possess property Np for all t >> 0. This gives a positive answer to a conjecture of Geramita and Gimigliano. Our bound for the values t is better than the conjectural value, which is σ(Z) + p.7 pagesAlgebraic GeometryCommutative AlgebraRings and Algebras14E25; 14J26; 13D02text