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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paper:paper_03730956_v66_n4_p1583_Molinuevo2023-06-08T15:37:51Z Unfoldings and deformations of rational and logarithmic foliations Molinuevo, Ariel Codimension one Deformations Foliations Unfoldings 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. Fil:Molinuevo, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03730956_v66_n4_p1583_Molinuevo http://hdl.handle.net/20.500.12110/paper_03730956_v66_n4_p1583_Molinuevo |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Codimension one Deformations Foliations Unfoldings |
| spellingShingle |
Codimension one Deformations Foliations Unfoldings Molinuevo, Ariel Unfoldings and deformations of rational and logarithmic foliations |
| topic_facet |
Codimension one Deformations Foliations Unfoldings |
| description |
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. |
| author |
Molinuevo, Ariel |
| author_facet |
Molinuevo, Ariel |
| author_sort |
Molinuevo, Ariel |
| title |
Unfoldings and deformations of rational and logarithmic foliations |
| title_short |
Unfoldings and deformations of rational and logarithmic foliations |
| title_full |
Unfoldings and deformations of rational and logarithmic foliations |
| title_fullStr |
Unfoldings and deformations of rational and logarithmic foliations |
| title_full_unstemmed |
Unfoldings and deformations of rational and logarithmic foliations |
| title_sort |
unfoldings and deformations of rational and logarithmic foliations |
| publishDate |
2016 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03730956_v66_n4_p1583_Molinuevo http://hdl.handle.net/20.500.12110/paper_03730956_v66_n4_p1583_Molinuevo |
| work_keys_str_mv |
AT molinuevoariel unfoldingsanddeformationsofrationalandlogarithmicfoliations |
| _version_ |
1768545191323500544 |