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Abstract:

We study codimension one foliations in projective space ℙn over ℂ by looking at its first order perturbations: unfoldings and deformations. We give special attention to foliations of rational and logarithmic type. For a differential form ω defining a codimension one foliation, we present a graded module 𝕌(ω), related to the first order unfoldings of ω. If ω is a generic form of rational or logarithmic type, as a first application of the construction of 𝕌(ω), we classify the first order deformations that arise from first order unfoldings. Then, we count the number of isolated points in the singular set of ω, in terms of a Hilbert polynomial associated to 𝕌(ω). We review the notion of regularity of ω in terms of a long complex of graded modules that we also introduce in this work. We use this complex to prove that, for generic rational and logarithmic foliations, ω is regular if and only if every unfolding is trivial up to isomorphism. © 2016, Association des Annales de l'Institut Fourier. All rights reserved.

Registro:

Documento: Artículo
Título:Unfoldings and deformations of rational and logarithmic foliations
Autor:Molinuevo, A.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, CP C1428EGA, Argentina
Palabras clave:Codimension one; Deformations; Foliations; Unfoldings
Año:2016
Volumen:66
Número:4
Página de inicio:1583
Página de fin:1613
DOI: http://dx.doi.org/10.5802/aif.3044
Título revista:Annales de l'Institut Fourier
Título revista abreviado:Ann. Inst. Fourier
ISSN:03730956
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03730956_v66_n4_p1583_Molinuevo

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Citas:

---------- APA ----------
(2016) . Unfoldings and deformations of rational and logarithmic foliations. Annales de l'Institut Fourier, 66(4), 1583-1613.
http://dx.doi.org/10.5802/aif.3044
---------- CHICAGO ----------
Molinuevo, A. "Unfoldings and deformations of rational and logarithmic foliations" . Annales de l'Institut Fourier 66, no. 4 (2016) : 1583-1613.
http://dx.doi.org/10.5802/aif.3044
---------- MLA ----------
Molinuevo, A. "Unfoldings and deformations of rational and logarithmic foliations" . Annales de l'Institut Fourier, vol. 66, no. 4, 2016, pp. 1583-1613.
http://dx.doi.org/10.5802/aif.3044
---------- VANCOUVER ----------
Molinuevo, A. Unfoldings and deformations of rational and logarithmic foliations. Ann. Inst. Fourier. 2016;66(4):1583-1613.
http://dx.doi.org/10.5802/aif.3044