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Abstract:

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.

Registro:

Documento: Artículo
Título:Families of distributions and pfaff systems under duality
Autor:Quallbrunn, F.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, Buenos Aires, Argentina
Palabras clave:Algebraic foliations; Coherent sheaves; Flat families; Kupka singularities; Moduli spaces
Año:2015
Volumen:11
Página de inicio:164
Página de fin:189
DOI: http://dx.doi.org/10.5427/jsing.2015.11g
Título revista:Journal of Singularities
Título revista abreviado:J. Singularities
ISSN:19492006
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19492006_v11_n_p164_Quallbrunn

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Citas:

---------- APA ----------
(2015) . Families of distributions and pfaff systems under duality. Journal of Singularities, 11, 164-189.
http://dx.doi.org/10.5427/jsing.2015.11g
---------- CHICAGO ----------
Quallbrunn, F. "Families of distributions and pfaff systems under duality" . Journal of Singularities 11 (2015) : 164-189.
http://dx.doi.org/10.5427/jsing.2015.11g
---------- MLA ----------
Quallbrunn, F. "Families of distributions and pfaff systems under duality" . Journal of Singularities, vol. 11, 2015, pp. 164-189.
http://dx.doi.org/10.5427/jsing.2015.11g
---------- VANCOUVER ----------
Quallbrunn, F. Families of distributions and pfaff systems under duality. J. Singularities. 2015;11:164-189.
http://dx.doi.org/10.5427/jsing.2015.11g