2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75897This paper shows the affirmative answer to the local Nash problem for a toric singularity and analytically pretoric singularity. As a corollary we obtain the affirmative answer to the local Nash problem for a quasi-ordinary singularity.to appear in Annales de l'Institute FourierAlgebraic Geometry14J17, 14M25The Local Nash problem on arc families of singularitiestext