Abstract
We generalize Frobenius singular theorem due to Malgrange, for a large class of codimension one holomorphic foliations on singular analytic subsets of ℂN.
Similar content being viewed by others
References
J.M. Aroca, H. Hironaka and J.L. Vicente. Introduction to the theory of infinitely near singular points. The theory of maximal contact. Desingularization theorems. Mem. Mat. Inst. Jorge Juan, 28, 29, 30. Madrid CSIC (1977).
C. Banica and O. Stanasila. Méthodes algébriques dans la théorie globale des espaces complexes. 3ème edition. Collection Varia Mathematica. Gauthier-Villars (1977).
D. Barlet and J. Magnuson. Familles analytiques de cycles, chapter Prolongement analytique; book to appear.
C. Camacho and P. Sad. Invariant varieties through singularities of holomorphic vector fields. Ann. of Math., 115 (1982), 579–595.
D. Cerveau, E. Ghys, N. Sibony and J.C. Yoccoz. Dynamique et géométrie complexes. Panoramas et Synthèses, 8 (1999), SMF.
C. Godbillon. Feuilletages: Études géométriques. With a preface by G. Reeb. Progress in Mathematics, 98 (1991), Birkhäuser Verlag, Basel.
H. Laufer. Normal two dimensional singularities. Ann. of Math. Studies, Princeton (1971).
E.J.N. Looijenga. Isolated Singular Points of Complete Intersections. London Math. Soc. Lecture Note Series 77, Cambridge University Press (1984).
A. Lins Neto. A note on projective Levi flats and minimal sets of algebraic foliations. Annales de L’Institut Fourier, tome 49, fasc. 4, 1369–1385 (1999).
A. Lins Neto and B.A. Scárdua. Folheações Algébricas Complexas. 21o Colóquio Brasileiro de Matemática, IMPA (1997).
B. Malgrange. Frobenius avec singularités I. Codimension un. Publ. Math. IHES, 46 (1976), 163–173.
J.F. Mattei and R. Moussu. Holonomie et intégrales premières. Ann. Ec. Norm. Sup., 13 (1980), 469–523.
M. Miyanishi. Algebraic Geometry. Transl. of the AMS vol. 136 (1994).
R. Moussu. Sur l’existence d’intégrales premières. Ann. Inst. Fourier, 26(2) (1976), 171–220.
K. Saito. On a Generalization of De-Rham Lemma. Ann. Inst. Fourier, 26(2) (1976), 165–170.
T. Suwa. Indices of vector fields and residues of holomorphic singular foliations. Hermann (1998).
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was partially supported by Pronex.
About this article
Cite this article
Cerveau, D., Lins Neto, A. Frobenius theorem for foliations on singular varieties. Bull Braz Math Soc, New Series 39, 447–469 (2008). https://doi.org/10.1007/s00574-008-0016-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00574-008-0016-2