2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110119In this paper we find a formula for the length of a finitely supported complete ideal in terms of the order of the strict transform of the ideal. This formula was known for complete ideals of height two in a two dimensional regular local ring and was proved independently by Hoskin and Deligne. Several consequences are deduced from this formula.23 pages. to appear in Journal of AlgebraCommutative AlgebraAlgebraic Geometry13B22, 13B22, 14E15text