2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119346In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two-dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.This manuscript is the doctoral thesis of the author submitted to the University of Helsinki. The thesis was supervised by Eero HyryCommutative AlgebraAlgebraic Geometry13H05 (Primary) 14B05 (Secondary)text