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

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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,...

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Detalles Bibliográficos
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
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spelling On the topology of the complement of a singular plane curve in the classification of singular holomorphic foliations of codimension oneSobre la topología del complemento de una curva singular plana en la clasificación de foliaciones holomorfas singulares de codimensión unoNeciosup Puican, HernánNeciosup Puican, HernánGrupo fundamentaholonomía proyectivafoliaciones singularesFundamental groupprojective holonomysingular foliationsIn 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]. En este artículo, estudiamos el papel del grupo fundamental del complemento de una curva plana afín en la clasificación analítica de foliaciones singulares de codimensión uno en (C3, 0). Nos enfocamos en obtener una representación adecuada del grupo fundamental del complemento de una curva plana afín particular, utilizando la monodromía de trenzas y el método de Zariski-Van Kampen. La imagen de este grupo, por la representación de holomonía de la foliación, es conocida como el grupo de holonomía de la foliación y la conjugación analítica de estos grupos equivale a la clasificación analítica de foliaciones holomorfas singulares cuspidales casi homogéneas de tipo admisible sobre (C3, 0) [6]. Universidad Nacional Mayor de San Marcos, Facultad de Ciencias Matemáticas2023-06-30info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/2506810.15381/pesquimat.v26i1.25068Pesquimat; Vol. 26 No. 1 (2023); 88-96Pesquimat; Vol. 26 Núm. 1 (2023); 88-961609-84391560-912Xreponame:Revistas - Universidad Nacional Mayor de San Marcosinstname:Universidad Nacional Mayor de San Marcosinstacron:UNMSMspahttps://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/25068/19752Derechos de autor 2023 Hernán Neciosup Puicanhttp://creativecommons.org/licenses/by-nc-sa/4.0info:eu-repo/semantics/openAccessoai:ojs.csi.unmsm:article/250682023-07-03T16:15:03Z
dc.title.none.fl_str_mv On the topology of the complement of a singular plane curve in the classification of singular holomorphic foliations of codimension one
Sobre la topología del complemento de una curva singular plana en la clasificación de foliaciones holomorfas singulares de codimensión uno
title On the topology of the complement of a singular plane curve in the classification of singular holomorphic foliations of codimension one
spellingShingle On the topology of the complement of a singular plane curve in the classification of singular holomorphic foliations of codimension one
Neciosup Puican, Hernán
Grupo fundamenta
holonomía proyectiva
foliaciones singulares
Fundamental group
projective holonomy
singular foliations
title_short On the topology of the complement of a singular plane curve in the classification of singular holomorphic foliations of codimension one
title_full On the topology of the complement of a singular plane curve in the classification of singular holomorphic foliations of codimension one
title_fullStr On the topology of the complement of a singular plane curve in the classification of singular holomorphic foliations of codimension one
title_full_unstemmed On the topology of the complement of a singular plane curve in the classification of singular holomorphic foliations of codimension one
title_sort On the topology of the complement of a singular plane curve in the classification of singular holomorphic foliations of codimension one
dc.creator.none.fl_str_mv Neciosup Puican, Hernán
Neciosup Puican, Hernán
author Neciosup Puican, Hernán
author_facet Neciosup Puican, Hernán
author_role author
dc.subject.none.fl_str_mv Grupo fundamenta
holonomía proyectiva
foliaciones singulares
Fundamental group
projective holonomy
singular foliations
topic Grupo fundamenta
holonomía proyectiva
foliaciones singulares
Fundamental group
projective holonomy
singular foliations
description 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].
publishDate 2023
dc.date.none.fl_str_mv 2023-06-30
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/25068
10.15381/pesquimat.v26i1.25068
url https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/25068
identifier_str_mv 10.15381/pesquimat.v26i1.25068
dc.language.none.fl_str_mv spa
language spa
dc.relation.none.fl_str_mv https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/25068/19752
dc.rights.none.fl_str_mv Derechos de autor 2023 Hernán Neciosup Puican
http://creativecommons.org/licenses/by-nc-sa/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Derechos de autor 2023 Hernán Neciosup Puican
http://creativecommons.org/licenses/by-nc-sa/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidad Nacional Mayor de San Marcos, Facultad de Ciencias Matemáticas
publisher.none.fl_str_mv Universidad Nacional Mayor de San Marcos, Facultad de Ciencias Matemáticas
dc.source.none.fl_str_mv Pesquimat; Vol. 26 No. 1 (2023); 88-96
Pesquimat; Vol. 26 Núm. 1 (2023); 88-96
1609-8439
1560-912X
reponame:Revistas - Universidad Nacional Mayor de San Marcos
instname:Universidad Nacional Mayor de San Marcos
instacron:UNMSM
instname_str Universidad Nacional Mayor de San Marcos
instacron_str UNMSM
institution UNMSM
reponame_str Revistas - Universidad Nacional Mayor de San Marcos
collection Revistas - Universidad Nacional Mayor de San Marcos
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 13.949927
On the topology of the complement of a singular plane curve in the classification of singular holomorphic foliations of codimension one
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