Linear holonomy groups of algebraic solutions of polynomial differential equations
Sad, Paulo
Annales de l'Institut Fourier, Tome 47 (1997), p. 123-138 / Harvested from Numdam

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},
     volume = {47},
     year = {1997},
     pages = {123-138},
     doi = {10.5802/aif.1562},
     mrnumber = {98c:32046},
     zbl = {0861.32019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 123-138. doi : 10.5802/aif.1562. http://gdmltest.u-ga.fr/item/AIF_1997__47_1_123_0/

[1] C. Camacho and P. Sad, Invariant Varieties through Singularities of Holomorphic Vector Fields, Ann. of Math., 115 (1982). | MR 83m:58062 | Zbl 0503.32007

[2] H. Cartan, Sur les Fonctions de Deux Variables Complexes, Bull. des Sci. Math., 54 (1930). | JFM 56.0981.04

[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 90b:58220 | Zbl 0681.58032

[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 34 #7789 | Zbl 0175.36801

[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 0194.40102

[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 88m:57036 | Zbl 0647.57017

[8] J. Muciño, Deformations of Holomorphic Foliations having a Meromorphic First Integral, J. Reine Angew. Math., 461 (1995). | MR 96e:32026 | Zbl 0816.32022

[9] Y. Siu, Techniques of Extension of Analytic Objects, M. Dekker, 1974. | MR 50 #13600 | Zbl 0294.32007