no. 1
Linear holonomy groups of algebraic solutions of polynomial differential equations
Annales de l'Institut Fourier, Tome 47 (1997) no. 1, pp. 123-138.

On étude la réalisation des sous-groupes de C * comme groupes d’holonomie linéaire de courbes algébriques qui sont invariantes pour les feuilletages de CP(2).

We consider the problem of realization of a linear subgroup of C * as the linear holonomy group of an algebraic curve which is a leaf of a foliation of CP(2).

@article{AIF_1997__47_1_123_0,
     author = {Sad, Paulo},
     title = {Linear holonomy groups of algebraic solutions of polynomial differential equations},
     journal = {Annales de l'Institut Fourier},
     pages = {123--138},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {47},
     number = {1},
     year = {1997},
     doi = {10.5802/aif.1562},
     mrnumber = {98c:32046},
     zbl = {0861.32019},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1562/}
}
TY  - JOUR
AU  - Sad, Paulo
TI  - Linear holonomy groups of algebraic solutions of polynomial differential equations
JO  - Annales de l'Institut Fourier
PY  - 1997
SP  - 123
EP  - 138
VL  - 47
IS  - 1
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1562/
DO  - 10.5802/aif.1562
LA  - en
ID  - AIF_1997__47_1_123_0
ER  - 
%0 Journal Article
%A Sad, Paulo
%T Linear holonomy groups of algebraic solutions of polynomial differential equations
%J Annales de l'Institut Fourier
%D 1997
%P 123-138
%V 47
%N 1
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.1562/
%R 10.5802/aif.1562
%G en
%F AIF_1997__47_1_123_0
Sad, Paulo. Linear holonomy groups of algebraic solutions of polynomial differential equations. Annales de l'Institut Fourier, Tome 47 (1997) no. 1, pp. 123-138. doi : 10.5802/aif.1562. http://www.numdam.org/articles/10.5802/aif.1562/

[1] C. Camacho and P. Sad, Invariant Varieties through Singularities of Holomorphic Vector Fields, Ann. of Math., 115 (1982). | MR | Zbl

[2] H. Cartan, Sur les Fonctions de Deux Variables Complexes, Bull. des Sci. Math., 54 (1930). | JFM

[3] X. Gómez-Mont and J. Muciño, Persistent Cycles for Holomorphic Foliations Having a Meromorphic First Integral, Lect. Notes in Math., 1345, Springer-Verlag (1988). | MR | Zbl

[4] H. Grauert and R. Remmert, Theory of Stein Spaces, Springer-Verlag, 1977.

[5] R. Gunning, Lectures on Riemann Surfaces, Princeton Univ. Press, 1966. | MR | Zbl

[6] Y. Ilyashenko, The Origin of Limit Cycles under Pertubation of the Equation dw/dz = Rz/Rw, where R(z, w) is a Polynomial, Math. USSR Sbornik, 7 (1969). | Zbl

[7] A. Lins Neto, Complex Codimension One Foliations Leaving a Compact Submanifold Invariant, in Dynamical Systems and Bifurcation Theory, Pitman Research Notes in Math. Series, 160 (1987). | MR | Zbl

[8] J. Muciño, Deformations of Holomorphic Foliations having a Meromorphic First Integral, J. Reine Angew. Math., 461 (1995). | MR | Zbl

[9] Y. Siu, Techniques of Extension of Analytic Objects, M. Dekker, 1974. | MR | Zbl

Cité par Sources :