2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228238A theory of simultaneous resolution of singularities for families of embedded varieties (over a field of characteristic zero) parametrized by the spectrum of a suitable artinian ring, and compatible with a given algorithm of resolution, is presented. As usually, this a simple consequence of a similar theory for analogous families of basic objects, to which the main portion of this article is devoted.Algebraic Geometry14B05;14D99text