On the topology of the complement of a singular plane curve in the classification of singular holomorphic foliations of codimension one

• Autor: Neciosup Puican, Hernán
• Formato: artículo
• Fecha de Publicación: 2023
• Institución: Universidad Nacional Mayor de San Marcos
• Repositorio: Revistas - Universidad Nacional Mayor de San Marcos
• Lenguaje: español
• OAI Identifier: oai:ojs.csi.unmsm:article/25068
• Enlace del recurso: https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/25068
• Nivel de acceso: acceso abierto
• Materia: Grupo fundamenta; holonomía proyectiva; foliaciones singulares; Fundamental group; projective holonomy; singular foliations

In this article, we study the role of the fundamental group of the complement of an affine plane curve in the analytic classification of singular codimension-one foliations in (C3, 0). We focus on obtaining an adequate representation of the fundamental group of a particular affine plane curve complement, using braid monodromy and the Zariski-Van Kampen method. The image of this group, under the holonomy representation of the foliation, is known as the holonomy group of the foliation and the analytic conjugacy of these groups is equivalent to the analytic classification of almost homogeneous cuspidal singular holomorphic foliations of admissible type on (C3, 0) [6].