2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139553Let Z be a fat point scheme in P^2 supported on general points. Here we prove that if the multiplicities are at most 3 and the length of Z is sufficiently high then the number of generators of the homogeneous ideal I_Z in each degree is as small as numerically possible. Since it is known that Z has maximal Hilbert function, this implies that Z has the expected minimal free resolution.18 pagesAlgebraic GeometryCommutative Algebra14N05text