2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149856Let E be a torsion-free sheaf on P2. We give an effective method which uses the Hilbert function of E to construct a weak version of the Harder-Narasimhan filtration of a torsion-free sheaf on P2 subject only to the condition that E be sufficiently general among sheaves with that Hilbert function. This algorithm uses on a generalization of Davis' decomposition lemma to higher rank.14 pages, LATeX 2.09Algebraic Geometrytext