Unfoldings and deformations of rational and logarithmic foliations
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 mo...
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Association des Annales de l'Institut Fourier
2016
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| 100 | 1 | |a Molinuevo, A. | |
| 245 | 1 | 0 | |a Unfoldings and deformations of rational and logarithmic foliations |
| 260 | |b Association des Annales de l'Institut Fourier |c 2016 | ||
| 270 | 1 | 0 | |m Molinuevo, A.; Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Argentina; email: arielmolinuevo@gmail.com |
| 506 | |2 openaire |e Política editorial | ||
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| 520 | 3 | |a 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. |l eng | |
| 536 | |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas | ||
| 536 | |a Detalles de la financiación: The author was fully supported by CONICET, Argentina. | ||
| 593 | |a Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, CP C1428EGA, Argentina | ||
| 690 | 1 | 0 | |a CODIMENSION ONE |
| 690 | 1 | 0 | |a DEFORMATIONS |
| 690 | 1 | 0 | |a FOLIATIONS |
| 690 | 1 | 0 | |a UNFOLDINGS |
| 773 | 0 | |d Association des Annales de l'Institut Fourier, 2016 |g v. 66 |h pp. 1583-1613 |k n. 4 |p Ann. Inst. Fourier |x 03730956 |w (AR-BaUEN)CENRE-239 |t Annales de l'Institut Fourier | |
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