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
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/103603
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:03:10Zoai: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:34982025-09-29 10:03:10.485CONICET 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 |
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2018-12 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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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 |
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eng |
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eng |
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openAccess |
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application/pdf application/zip application/pdf |
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International Press Boston |
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International Press Boston |
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