2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77861Let X be a complex algebraic variety, and L(X) be the scheme of formal arcs in X. Let f be an arc whose image is not contained in the singularities of X. We show that the formal neighborhood of f in L(X) admits a decomposition into a product of an infinite-dimensional smooth piece, and a piece isomorphic to the formal neighborhood of a closed point of a scheme of finite type.12 pages, AMS-LaTeXAlgebraic Geometry14B20text