Analytic semiroots for plane branches and singular foliations

The analytic moduli of equisingular plane branches has the semimodule of differential values as the most relevant system of discrete invariants. Focusing in the case of cusps, the minimal system of generators of this semimodule is reached by the differential values attached to the differential 1-for...

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Detalhes bibliográficos
Autores: Cano Torres, Felipe, Corral Pérez, Nuria|||0000-0003-3183-8386, Senovilla Sanz, David
Formato: artículo
Fecha de publicación:2023
País:España
Recursos:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/31834
Acesso em linha:https://hdl.handle.net/10902/31834
Access Level:acceso abierto
Palavra-chave:Analytic invariants
Equisingularity
Semimodule
Cusp
Standard basis
Differential values
Dicritical foliation
Analytic semiroots
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spelling Analytic semiroots for plane branches and singular foliationsCano Torres, FelipeCorral Pérez, Nuria|||0000-0003-3183-8386Senovilla Sanz, DavidAnalytic invariantsEquisingularitySemimoduleCuspStandard basisDifferential valuesDicritical foliationAnalytic semirootsThe analytic moduli of equisingular plane branches has the semimodule of differential values as the most relevant system of discrete invariants. Focusing in the case of cusps, the minimal system of generators of this semimodule is reached by the differential values attached to the differential 1-forms of the so-called standard bases. We can complete a standard basis to an extended one by adding a last differential 1-form that has the considered cusp as invariant branch and the "correct" divisorial order. The elements of such extended standard bases have the "cuspidal" divisor as a "totally dicritical divisor" and hence they define packages of plane branches that are equisingular to the initial one. These are the analytic semiroots. In this paper we prove that the extended standard bases are well structured from this geometrical and foliated viewpoint, in the sense that the semimodules of differential values of the branches in the dicritical packages are described just by a truncation of the list of generators of the initial semimodule at the corresponding differential value. In particular they have all the same semimodule of differential values.The authors are supported by the Spanish research project PID2019-105621GB-I00/AEI/10.13039/ 501100011033 funded by the Agencia Estatal de Investigación — Ministerio de Ciencia e Innovación. David Senovilla-Sanz is also supported by a predoctoral contract "Concepción Arenal" of the Universidad de Cantabria.SpringerUniversidad de Cantabria20232023-05-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/31834Bulletin of the Brazilian Mathematical Society, New Series, 2023, 54(2), 27reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/318342026-06-02T12:39:31Z
dc.title.none.fl_str_mv Analytic semiroots for plane branches and singular foliations
title Analytic semiroots for plane branches and singular foliations
spellingShingle Analytic semiroots for plane branches and singular foliations
Cano Torres, Felipe
Analytic invariants
Equisingularity
Semimodule
Cusp
Standard basis
Differential values
Dicritical foliation
Analytic semiroots
title_short Analytic semiroots for plane branches and singular foliations
title_full Analytic semiroots for plane branches and singular foliations
title_fullStr Analytic semiroots for plane branches and singular foliations
title_full_unstemmed Analytic semiroots for plane branches and singular foliations
title_sort Analytic semiroots for plane branches and singular foliations
dc.creator.none.fl_str_mv Cano Torres, Felipe
Corral Pérez, Nuria|||0000-0003-3183-8386
Senovilla Sanz, David
author Cano Torres, Felipe
author_facet Cano Torres, Felipe
Corral Pérez, Nuria|||0000-0003-3183-8386
Senovilla Sanz, David
author_role author
author2 Corral Pérez, Nuria|||0000-0003-3183-8386
Senovilla Sanz, David
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Analytic invariants
Equisingularity
Semimodule
Cusp
Standard basis
Differential values
Dicritical foliation
Analytic semiroots
topic Analytic invariants
Equisingularity
Semimodule
Cusp
Standard basis
Differential values
Dicritical foliation
Analytic semiroots
description The analytic moduli of equisingular plane branches has the semimodule of differential values as the most relevant system of discrete invariants. Focusing in the case of cusps, the minimal system of generators of this semimodule is reached by the differential values attached to the differential 1-forms of the so-called standard bases. We can complete a standard basis to an extended one by adding a last differential 1-form that has the considered cusp as invariant branch and the "correct" divisorial order. The elements of such extended standard bases have the "cuspidal" divisor as a "totally dicritical divisor" and hence they define packages of plane branches that are equisingular to the initial one. These are the analytic semiroots. In this paper we prove that the extended standard bases are well structured from this geometrical and foliated viewpoint, in the sense that the semimodules of differential values of the branches in the dicritical packages are described just by a truncation of the list of generators of the initial semimodule at the corresponding differential value. In particular they have all the same semimodule of differential values.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-05-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10902/31834
url https://hdl.handle.net/10902/31834
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv Bulletin of the Brazilian Mathematical Society, New Series, 2023, 54(2), 27
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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