Families of distributions and pfaff systems under duality

A singular distribution on a non-singular variety X can be defined either by a subsheaf D ⊆ TX of the tangent sheaf, or by the zeros of a subsheaf D0 ⊆ Ω1 X of 1-forms, that is, a Pfaff system. Although both definitions are equivalent under mild conditions on D, they give rise, in general, to non-eq...

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Autor principal: Quallbrunn, F.
Formato: JOUR
Materias:
Algebraic foliations
Coherent sheaves
Flat families
Kupka singularities
Moduli spaces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_19492006_v11_n_p164_Quallbrunn
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_19492006_v11_n_p164_Quallbrunn2023-10-03T16:37:14Z Families of distributions and pfaff systems under duality Quallbrunn, F. Algebraic foliations Coherent sheaves Flat families Kupka singularities Moduli spaces A singular distribution on a non-singular variety X can be defined either by a subsheaf D ⊆ TX of the tangent sheaf, or by the zeros of a subsheaf D0 ⊆ Ω1 X of 1-forms, that is, a Pfaff system. Although both definitions are equivalent under mild conditions on D, they give rise, in general, to non-equivalent notions of flat families of distributions. In this work we investigate conditions under which both notions of flat families are equivalent. In the last sections we focus on the case where the distribution is integrable, and we use our results to generalize a theorem of Cukierman and Pereira. © 2015, Worldwide Center of Mathematics. All Rights Reserved. Fil:Quallbrunn, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_19492006_v11_n_p164_Quallbrunn
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Algebraic foliations
Coherent sheaves
Flat families
Kupka singularities
Moduli spaces
spellingShingle Algebraic foliations
Coherent sheaves
Flat families
Kupka singularities
Moduli spaces
Quallbrunn, F.
Families of distributions and pfaff systems under duality
topic_facet Algebraic foliations
Coherent sheaves
Flat families
Kupka singularities
Moduli spaces
description A singular distribution on a non-singular variety X can be defined either by a subsheaf D ⊆ TX of the tangent sheaf, or by the zeros of a subsheaf D0 ⊆ Ω1 X of 1-forms, that is, a Pfaff system. Although both definitions are equivalent under mild conditions on D, they give rise, in general, to non-equivalent notions of flat families of distributions. In this work we investigate conditions under which both notions of flat families are equivalent. In the last sections we focus on the case where the distribution is integrable, and we use our results to generalize a theorem of Cukierman and Pereira. © 2015, Worldwide Center of Mathematics. All Rights Reserved.
format JOUR
author Quallbrunn, F.
author_facet Quallbrunn, F.
author_sort Quallbrunn, F.
title Families of distributions and pfaff systems under duality
title_short Families of distributions and pfaff systems under duality
title_full Families of distributions and pfaff systems under duality
title_fullStr Families of distributions and pfaff systems under duality
title_full_unstemmed Families of distributions and pfaff systems under duality
title_sort families of distributions and pfaff systems under duality
url http://hdl.handle.net/20.500.12110/paper_19492006_v11_n_p164_Quallbrunn
work_keys_str_mv AT quallbrunnf familiesofdistributionsandpfaffsystemsunderduality
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