Formal and Analytic normal forms of germs of holomorphic nondicritic foliations
Journal of Singularities, Tome 9 (2014), pp. 168-192
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We consider the class V_n of germs of holomorphic vector fields in (C^2,0) with vanishing (n-1)-jet at the origin, n > 1. For generic germs v in V_2 we prove the existence of an analytical orbital normal form whose orbital formal normal form has the form v_{c,b} given in a previous paper of the current authors. Furthermore, fixing one representative vˆ of the analytic class of a germ v in V_2 having the y-axis invariant, the corresponding formal normal form vˆ_{c, bˆ} is analytic and unique (under strict orbital equivalence). Moreover for generic v in V_n, n>1, we give a preliminary orbital analytic normal form which is polynomial and of degree at most n in the y-variable.
@article{10_5427_jsing_2014_9m,
author = {L. Ortiz-Bobadilla and E. Rosales-Gonz\'alez, and S. M. Voronin},
title = {Formal and {Analytic} normal forms of germs of holomorphic nondicritic foliations},
journal = {Journal of Singularities},
pages = {168--192},
publisher = {mathdoc},
volume = {9},
year = {2014},
doi = {10.5427/jsing.2014.9m},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.9m/}
}
TY - JOUR AU - L. Ortiz-Bobadilla AU - E. Rosales-González, AU - S. M. Voronin TI - Formal and Analytic normal forms of germs of holomorphic nondicritic foliations JO - Journal of Singularities PY - 2014 SP - 168 EP - 192 VL - 9 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.9m/ DO - 10.5427/jsing.2014.9m ID - 10_5427_jsing_2014_9m ER -
%0 Journal Article %A L. Ortiz-Bobadilla %A E. Rosales-González, %A S. M. Voronin %T Formal and Analytic normal forms of germs of holomorphic nondicritic foliations %J Journal of Singularities %D 2014 %P 168-192 %V 9 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.9m/ %R 10.5427/jsing.2014.9m %F 10_5427_jsing_2014_9m
L. Ortiz-Bobadilla; E. Rosales-González,; S. M. Voronin. Formal and Analytic normal forms of germs of holomorphic nondicritic foliations. Journal of Singularities, Tome 9 (2014), pp. 168-192. doi: 10.5427/jsing.2014.9m
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