Monomial generators of complete planar ideals

We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the minimal log-resolution of the ideal. Furthermore, the monomial e...

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Autores: Alberich Carramiñana, Maria|||0000-0003-2749-4875, Álvarez Montaner, Josep|||0000-0001-6793-368X, Blanco Fernández, Guillem|||0000-0002-6073-4175
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/180848
Acceso en línea:https://hdl.handle.net/2117/180848
https://dx.doi.org/10.1142/S0219498821500328
Access Level:acceso abierto
Palabra clave:Algebraic geometry
Commutative algebra
Complete ideals
aximal contact curves
Multiplier ideals
Geometria algebraica
Àlgebra commutativa
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
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spelling Monomial generators of complete planar idealsAlberich Carramiñana, Maria|||0000-0003-2749-4875Álvarez Montaner, Josep|||0000-0001-6793-368XBlanco Fernández, Guillem|||0000-0002-6073-4175Algebraic geometryCommutative algebraComplete idealsaximal contact curvesMultiplier idealsGeometria algebraicaÀlgebra commutativaÀrees temàtiques de la UPC::Matemàtiques i estadística::ÀlgebraWe provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the minimal log-resolution of the ideal. Furthermore, the monomial expression given by our method is an equisingularity invariant of the ideal. As an outcome, we provide a geometric method to compute the integral closure of a planar ideal and we apply our algorithm to some families of complete idealsPeer Reviewed20202020-01-0120202020-03-23journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/180848https://dx.doi.org/10.1142/S0219498821500328reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1808482026-05-27T15:37:01Z
dc.title.none.fl_str_mv Monomial generators of complete planar ideals
title Monomial generators of complete planar ideals
spellingShingle Monomial generators of complete planar ideals
Alberich Carramiñana, Maria|||0000-0003-2749-4875
Algebraic geometry
Commutative algebra
Complete ideals
aximal contact curves
Multiplier ideals
Geometria algebraica
Àlgebra commutativa
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
title_short Monomial generators of complete planar ideals
title_full Monomial generators of complete planar ideals
title_fullStr Monomial generators of complete planar ideals
title_full_unstemmed Monomial generators of complete planar ideals
title_sort Monomial generators of complete planar ideals
dc.creator.none.fl_str_mv Alberich Carramiñana, Maria|||0000-0003-2749-4875
Álvarez Montaner, Josep|||0000-0001-6793-368X
Blanco Fernández, Guillem|||0000-0002-6073-4175
author Alberich Carramiñana, Maria|||0000-0003-2749-4875
author_facet Alberich Carramiñana, Maria|||0000-0003-2749-4875
Álvarez Montaner, Josep|||0000-0001-6793-368X
Blanco Fernández, Guillem|||0000-0002-6073-4175
author_role author
author2 Álvarez Montaner, Josep|||0000-0001-6793-368X
Blanco Fernández, Guillem|||0000-0002-6073-4175
author2_role author
author
dc.subject.none.fl_str_mv Algebraic geometry
Commutative algebra
Complete ideals
aximal contact curves
Multiplier ideals
Geometria algebraica
Àlgebra commutativa
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
topic Algebraic geometry
Commutative algebra
Complete ideals
aximal contact curves
Multiplier ideals
Geometria algebraica
Àlgebra commutativa
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
description We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the minimal log-resolution of the ideal. Furthermore, the monomial expression given by our method is an equisingularity invariant of the ideal. As an outcome, we provide a geometric method to compute the integral closure of a planar ideal and we apply our algorithm to some families of complete ideals
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01
2020
2020-03-23
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/180848
https://dx.doi.org/10.1142/S0219498821500328
url https://hdl.handle.net/2117/180848
https://dx.doi.org/10.1142/S0219498821500328
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-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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