Par l’introduction d’un nouvel invariant appelé l’ensemble des glissements, nous donnons une classification stricte complète de la classe des germes de feuilletages holomorphes non dicritiques dont les indices de Camacho-Sad ne sont pas rationnels. Par ailleurs, nous allons montrer que, dans cette classe, le nouvel invariant est de détermination finie. Par conséquent, nous obtenons la détermination finie de la classe des feuilletages non dicritiques isoholonomiques et de feuilletages absolument dicritiques qui ont les mêmes applications de Dulac.
By introducing a new invariant called the set of slidings, we give a complete strict classification of the class of germs of non-dicritical holomorphic foliations in the plan whose Camacho-Sad indices are not rational. Moreover, we will show that, in this class, the new invariant is finitely determined. Consequently, the finite determination of the class of isoholonomic non-dicritical foliations and absolutely dicritical foliations that have the same Dulac maps is proved.
@article{AIF_2015__65_5_1897_0,
author = {Truong, Hong Minh},
title = {Sliding invariants and classification of singular holomorphic foliations in the plane},
journal = {Annales de l'Institut Fourier},
volume = {65},
year = {2015},
pages = {1897-1920},
doi = {10.5802/aif.2976},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2015__65_5_1897_0}
}
Truong, Hong Minh. Sliding invariants and classification of singular holomorphic foliations in the plane. Annales de l'Institut Fourier, Tome 65 (2015) pp. 1897-1920. doi : 10.5802/aif.2976. http://gdmltest.u-ga.fr/item/AIF_2015__65_5_1897_0/
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