The Kupka Scheme and Unfoldings

Autores
Massri, Cesar Dario; Molinuevo, Ariel; Quallbrunn, Federico
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let ω be a differential 1-form defining an algebraic foliation of codimension 1 in projective space. In this article we use commutative algebra to study the singular locus of ω through its ideal of definition. Then, we expose the relation between the ideal defining the Kupka components of the singular set of ω and the first order unfoldings of ω. Exploiting this relation, we show that the set of Kupka points of ω is generically not empty. As an application of these results, we can compute the ideal of first order unfoldings for some known components of the space of foliations.
Fil: Massri, Cesar Dario. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Molinuevo, Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Quallbrunn, Federico. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Unfoldings of foliations
Kupka set
algebraic foliations
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/103603
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The Kupka Scheme and UnfoldingsMassri, Cesar DarioMolinuevo, ArielQuallbrunn, FedericoUnfoldings of foliationsKupka setalgebraic foliationshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let ω be a differential 1-form defining an algebraic foliation of codimension 1 in projective space. In this article we use commutative algebra to study the singular locus of ω through its ideal of definition. Then, we expose the relation between the ideal defining the Kupka components of the singular set of ω and the first order unfoldings of ω. Exploiting this relation, we show that the set of Kupka points of ω is generically not empty. As an application of these results, we can compute the ideal of first order unfoldings for some known components of the space of foliations.Fil: Massri, Cesar Dario. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Molinuevo, Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Quallbrunn, Federico. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaInternational Press Boston2018-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/103603Massri, Cesar Dario; Molinuevo, Ariel; Quallbrunn, Federico; The Kupka Scheme and Unfoldings; International Press Boston; Asian Journal of Mathematics; 22; 6; 12-2018; 1025-10461093-6106CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1509.07231info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:59:29Zoai:ri.conicet.gov.ar:11336/103603instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 14:59:29.624CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Kupka Scheme and Unfoldings
title The Kupka Scheme and Unfoldings
spellingShingle The Kupka Scheme and Unfoldings
Massri, Cesar Dario
Unfoldings of foliations
Kupka set
algebraic foliations
title_short The Kupka Scheme and Unfoldings
title_full The Kupka Scheme and Unfoldings
title_fullStr The Kupka Scheme and Unfoldings
title_full_unstemmed The Kupka Scheme and Unfoldings
title_sort The Kupka Scheme and Unfoldings
dc.creator.none.fl_str_mv Massri, Cesar Dario
Molinuevo, Ariel
Quallbrunn, Federico
author Massri, Cesar Dario
author_facet Massri, Cesar Dario
Molinuevo, Ariel
Quallbrunn, Federico
author_role author
author2 Molinuevo, Ariel
Quallbrunn, Federico
author2_role author
author
dc.subject.none.fl_str_mv Unfoldings of foliations
Kupka set
algebraic foliations
topic Unfoldings of foliations
Kupka set
algebraic foliations
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let ω be a differential 1-form defining an algebraic foliation of codimension 1 in projective space. In this article we use commutative algebra to study the singular locus of ω through its ideal of definition. Then, we expose the relation between the ideal defining the Kupka components of the singular set of ω and the first order unfoldings of ω. Exploiting this relation, we show that the set of Kupka points of ω is generically not empty. As an application of these results, we can compute the ideal of first order unfoldings for some known components of the space of foliations.
Fil: Massri, Cesar Dario. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Molinuevo, Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Quallbrunn, Federico. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Let ω be a differential 1-form defining an algebraic foliation of codimension 1 in projective space. In this article we use commutative algebra to study the singular locus of ω through its ideal of definition. Then, we expose the relation between the ideal defining the Kupka components of the singular set of ω and the first order unfoldings of ω. Exploiting this relation, we show that the set of Kupka points of ω is generically not empty. As an application of these results, we can compute the ideal of first order unfoldings for some known components of the space of foliations.
publishDate 2018
dc.date.none.fl_str_mv 2018-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/103603
Massri, Cesar Dario; Molinuevo, Ariel; Quallbrunn, Federico; The Kupka Scheme and Unfoldings; International Press Boston; Asian Journal of Mathematics; 22; 6; 12-2018; 1025-1046
1093-6106
CONICET Digital
CONICET
url http://hdl.handle.net/11336/103603
identifier_str_mv Massri, Cesar Dario; Molinuevo, Ariel; Quallbrunn, Federico; The Kupka Scheme and Unfoldings; International Press Boston; Asian Journal of Mathematics; 22; 6; 12-2018; 1025-1046
1093-6106
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1509.07231
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/zip
application/pdf
dc.publisher.none.fl_str_mv International Press Boston
publisher.none.fl_str_mv International Press Boston
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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