2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64548Nash proved that every irreducible component of the space of arcs through a singularity corresponds to an exceptional divisor that occurs on every resolution. He asked if the converse also holds: does every such exceptional divisor correspond to an arc family? We prove that the converse holds for toric singularities but fails in general.17 pagesAlgebraic Geometry14J17, 14M25, 14J10text