2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76466We clarify the question whether for a smooth curve of polynomials one can choose the roots smoothly and related questions. Applications to perturbation theory of operators are given.to appear Israel J. MathClassical Analysis and ODEsFunctional AnalysisSpectral Theory26C10, 47A55text