On étude la réalisation des sous-groupes de comme groupes d’holonomie linéaire de courbes algébriques qui sont invariantes pour les feuilletages de .
We consider the problem of realization of a linear subgroup of as the linear holonomy group of an algebraic curve which is a leaf of a foliation of .
@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] Invariant Varieties through Singularities of Holomorphic Vector Fields, Ann. of Math., 115 (1982). | MR 83m:58062 | Zbl 0503.32007
and ,[2] Sur les Fonctions de Deux Variables Complexes, Bull. des Sci. Math., 54 (1930). | JFM 56.0981.04
,[3] Persistent Cycles for Holomorphic Foliations Having a Meromorphic First Integral, Lect. Notes in Math., 1345, Springer-Verlag (1988). | MR 90b:58220 | Zbl 0681.58032
and ,[4] Theory of Stein Spaces, Springer-Verlag, 1977.
and ,[5] Lectures on Riemann Surfaces, Princeton Univ. Press, 1966. | MR 34 #7789 | Zbl 0175.36801
,[6] 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] 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] Deformations of Holomorphic Foliations having a Meromorphic First Integral, J. Reine Angew. Math., 461 (1995). | MR 96e:32026 | Zbl 0816.32022
,[9] Techniques of Extension of Analytic Objects, M. Dekker, 1974. | MR 50 #13600 | Zbl 0294.32007
,