2026-04-05T12:43:09Zhttps://recercat.cat/oai/request

oai:recercat.cat:2099.1/65412025-07-22T20:43:45Zcom_2072_1033col_2072_452951

Classification of plane germs: metric and valorative properties Abío Roig, Ignasi Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica Singularities (Mathematics) Curves, Plane. plane curves Singularitats (Matemàtica) Corbes planes Classificació AMS::14 Algebraic geometry::14H Curves In this memory we follow the geometric approach of Casas’ boof [1] for studying of the singularities of plane germs of curves, which updates Enriques’ works to modern standards and reviews the modern development of the theorey from the point of view of infinitely near points. This memory has a two sided goal: on one hand, we want to acquire skills with the tools and concepts of the singularity theory and the valuative theory, both the classical ones and the more recent ones. On the other hand, we want to study in depth the different implicit concepts and notions involved in the Favre and Jonsson’s new approach, such as the ultrametric space structure of the set of irreducible germs of plane curves and the tree structure of the valuations. 2008-06 Master thesis (pre-Bologna period) http://creativecommons.org/licenses/by-nc-sa/3.0/es/ Open Access Attribution-NonCommercial-ShareAlike 3.0 Spain Universitat Politècnica de Catalunya