The Kupka scheme and unfoldings

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 singul...

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Detalles Bibliográficos
Autores principales: Massri, C., Molinuevo, A., Quallbrunn, F.
Formato: SER
Materias:
Foliation
Kupka singularities
Unfoldings
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_10936106_v22_n6_p1025_Massri
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_10936106_v22_n6_p1025_Massri
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spelling todo:paper_10936106_v22_n6_p1025_Massri2023-10-03T16:05:01Z The Kupka scheme and unfoldings Massri, C. Molinuevo, A. Quallbrunn, F. Foliation Kupka singularities Unfoldings 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. © 2018 International Press. SER info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10936106_v22_n6_p1025_Massri
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Foliation
Kupka singularities
Unfoldings
spellingShingle Foliation
Kupka singularities
Unfoldings
Massri, C.
Molinuevo, A.
Quallbrunn, F.
The Kupka scheme and unfoldings
topic_facet Foliation
Kupka singularities
Unfoldings
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. © 2018 International Press.
format SER
author Massri, C.
Molinuevo, A.
Quallbrunn, F.
author_facet Massri, C.
Molinuevo, A.
Quallbrunn, F.
author_sort Massri, C.
title The Kupka scheme and unfoldings
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 kupka scheme and unfoldings
url http://hdl.handle.net/20.500.12110/paper_10936106_v22_n6_p1025_Massri
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AT molinuevoa thekupkaschemeandunfoldings
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AT massric kupkaschemeandunfoldings
AT molinuevoa kupkaschemeandunfoldings
AT quallbrunnf kupkaschemeandunfoldings
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