2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65675It is an open problem to determine the dimension of the space of homogeneous polynomials of a fixed degree vanishing at finitely many points in the projective plane to certain multiplicities. We present various aspects of this problem and a version of a known algorithm (originally due to M. Nagata) to compute this dimension for nine or less points. Our methods are completely elementary and only involve the representation theory of SL_2.Algebraic Geometrytext