Resolving singularities of curves with one toric morphism

We give an explicit positive answer, in the case of reduced curve singularities, to a question of B. Teissier about the existence of a toric embedded resolution after reembedding. In the case of a curve singularity pC,Oq contained in a non singular surface S such a reembedding may be defined in term...

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Detalles Bibliográficos
Autores: Felipe, Ana Belén de, González Pérez, Pedro Daniel, Mourtada, Hussein
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/71921
Acceso en línea:https://hdl.handle.net/20.500.14352/71921
Access Level:acceso abierto
Palabra clave:512.7
Divisorial valuations
Curve singularities
Generating sequences
Resolution of singularities
Toric geometry
Local tropicalization
Torific embedding
Geometria algebraica
1201.01 Geometría Algebraica
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spelling Resolving singularities of curves with one toric morphismFelipe, Ana Belén deGonzález Pérez, Pedro DanielMourtada, Hussein512.7Divisorial valuationsCurve singularitiesGenerating sequencesResolution of singularitiesToric geometryLocal tropicalizationTorific embeddingGeometria algebraica1201.01 Geometría AlgebraicaWe give an explicit positive answer, in the case of reduced curve singularities, to a question of B. Teissier about the existence of a toric embedded resolution after reembedding. In the case of a curve singularity pC,Oq contained in a non singular surface S such a reembedding may be defined in terms of a sequence of maximal contact curves associated to C. We prove that there exists a toric modification, after reembedding, which provides an embedded resolution of C. We use properties of the semivaluation space of S at O to describe how the the dual graph of the minimal embedded resolution of C may be seen on the local tropicalization of S associated to this reembedding.Springer NatureUniversidad Complutense de Madrid20222022-11-1520222022-11-15journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/71921reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Atribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/719212026-06-02T12:44:21Z
dc.title.none.fl_str_mv Resolving singularities of curves with one toric morphism
title Resolving singularities of curves with one toric morphism
spellingShingle Resolving singularities of curves with one toric morphism
Felipe, Ana Belén de
512.7
Divisorial valuations
Curve singularities
Generating sequences
Resolution of singularities
Toric geometry
Local tropicalization
Torific embedding
Geometria algebraica
1201.01 Geometría Algebraica
title_short Resolving singularities of curves with one toric morphism
title_full Resolving singularities of curves with one toric morphism
title_fullStr Resolving singularities of curves with one toric morphism
title_full_unstemmed Resolving singularities of curves with one toric morphism
title_sort Resolving singularities of curves with one toric morphism
dc.creator.none.fl_str_mv Felipe, Ana Belén de
González Pérez, Pedro Daniel
Mourtada, Hussein
author Felipe, Ana Belén de
author_facet Felipe, Ana Belén de
González Pérez, Pedro Daniel
Mourtada, Hussein
author_role author
author2 González Pérez, Pedro Daniel
Mourtada, Hussein
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 512.7
Divisorial valuations
Curve singularities
Generating sequences
Resolution of singularities
Toric geometry
Local tropicalization
Torific embedding
Geometria algebraica
1201.01 Geometría Algebraica
topic 512.7
Divisorial valuations
Curve singularities
Generating sequences
Resolution of singularities
Toric geometry
Local tropicalization
Torific embedding
Geometria algebraica
1201.01 Geometría Algebraica
description We give an explicit positive answer, in the case of reduced curve singularities, to a question of B. Teissier about the existence of a toric embedded resolution after reembedding. In the case of a curve singularity pC,Oq contained in a non singular surface S such a reembedding may be defined in terms of a sequence of maximal contact curves associated to C. We prove that there exists a toric modification, after reembedding, which provides an embedded resolution of C. We use properties of the semivaluation space of S at O to describe how the the dual graph of the minimal embedded resolution of C may be seen on the local tropicalization of S associated to this reembedding.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-11-15
2022
2022-11-15
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/20.500.14352/71921
url https://hdl.handle.net/20.500.14352/71921
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
Atribución 3.0 España
https://creativecommons.org/licenses/by/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
Atribución 3.0 España
https://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
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 15,301603

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