Approximate roots, toric resolutions and deformations of a plane branch

We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial f is an element of C{x}[y], defining a plane branch (C, 0), in the light of the toric embedded resolution of the branch. This leads to the definition of a class of (non-equisingular) deformations of a plane branc...

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Detalles Bibliográficos
Autor: González Pérez, Pedro Daniel
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/42247
Acceso en línea:https://hdl.handle.net/20.500.14352/42247
Access Level:acceso abierto
Palabra clave:512.76/.77
512.745.2
Generalized Tschirnhausen transformation
Newton-Puiseux expansion
hypersurface singularities
polar invariants
curves
irreducibility
approximate roots
deformations of a plane curve
equisingularity criterion
Álgebra
1201 Álgebra
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oai_identifier_str oai:docta.ucm.es:20.500.14352/42247
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repository_id_str
spelling Approximate roots, toric resolutions and deformations of a plane branchGonzález Pérez, Pedro Daniel512.76/.77512.745.2Generalized Tschirnhausen transformationNewton-Puiseux expansionhypersurface singularitiespolar invariantscurvesirreducibilityapproximate rootsdeformations of a plane curveequisingularity criterionÁlgebra1201 ÁlgebraWe analyze the expansions in terms of the approximate roots of a Weierstrass polynomial f is an element of C{x}[y], defining a plane branch (C, 0), in the light of the toric embedded resolution of the branch. This leads to the definition of a class of (non-equisingular) deformations of a plane branch (C, 0) supported on certain monomials in the approximate roots of f, which are essential in the study of Harnack smoothings of real plane branches by Risler and the author. Our results provide also a geometrical approach to Abhyankar's irreducibility criterion for power series in two variables and also a criterion to determine if a family of plane curves is equisingular to a plane branch.Math Soc JapanUniversidad Complutense de Madrid20102010-07-0120102010-07-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/42247reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/422472026-06-02T12:44:21Z
dc.title.none.fl_str_mv Approximate roots, toric resolutions and deformations of a plane branch
title Approximate roots, toric resolutions and deformations of a plane branch
spellingShingle Approximate roots, toric resolutions and deformations of a plane branch
González Pérez, Pedro Daniel
512.76/.77
512.745.2
Generalized Tschirnhausen transformation
Newton-Puiseux expansion
hypersurface singularities
polar invariants
curves
irreducibility
approximate roots
deformations of a plane curve
equisingularity criterion
Álgebra
1201 Álgebra
title_short Approximate roots, toric resolutions and deformations of a plane branch
title_full Approximate roots, toric resolutions and deformations of a plane branch
title_fullStr Approximate roots, toric resolutions and deformations of a plane branch
title_full_unstemmed Approximate roots, toric resolutions and deformations of a plane branch
title_sort Approximate roots, toric resolutions and deformations of a plane branch
dc.creator.none.fl_str_mv González Pérez, Pedro Daniel
author González Pérez, Pedro Daniel
author_facet González Pérez, Pedro Daniel
author_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 512.76/.77
512.745.2
Generalized Tschirnhausen transformation
Newton-Puiseux expansion
hypersurface singularities
polar invariants
curves
irreducibility
approximate roots
deformations of a plane curve
equisingularity criterion
Álgebra
1201 Álgebra
topic 512.76/.77
512.745.2
Generalized Tschirnhausen transformation
Newton-Puiseux expansion
hypersurface singularities
polar invariants
curves
irreducibility
approximate roots
deformations of a plane curve
equisingularity criterion
Álgebra
1201 Álgebra
description We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial f is an element of C{x}[y], defining a plane branch (C, 0), in the light of the toric embedded resolution of the branch. This leads to the definition of a class of (non-equisingular) deformations of a plane branch (C, 0) supported on certain monomials in the approximate roots of f, which are essential in the study of Harnack smoothings of real plane branches by Risler and the author. Our results provide also a geometrical approach to Abhyankar's irreducibility criterion for power series in two variables and also a criterion to determine if a family of plane curves is equisingular to a plane branch.
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-07-01
2010
2010-07-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/42247
url https://hdl.handle.net/20.500.14352/42247
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
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Math Soc Japan
publisher.none.fl_str_mv Math Soc Japan
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301629

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