Proximity inequalities and bounds for the degree of invariant curves by foliations of p£

Transactions of the American Mathematical Society

Volumn 349, Issue 6, 1997, Pages 2211-2228

  Campillo, Antonio ^a,b   Carnicer, Manuel M ^a,b  

^a UNIVERSITY OF VALLADOLID   (Spain)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21744432119     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-97-01898-9     Document Type: Article

References (15)

1. C. Camacho and P. Sad. Invariant varieties through singularities of holomorphic vector fields. Annals of Math., 115:579-595, 1982. MR 83m:58062
2. C. Camacho, A. Lins Neto, and P. Sad. Topological invariants and equidesingularization for holomorphic vector fields. Journal of Differential Geometry, 20:143-174, 1984. MR86d:58080
3. A. Campillo, G. Gonzalez-Sprinberg, and M. Lejeune. Enriques diagrams, resolutions and toric clusters. C.R. Acad. Sei. Paris, Serie I, 320:329-334, 1995. MR 95k:14018
4. F. Cano. Dicriticalness of a singular foliation. In X. Gomez-Mont, J. Seade, and A. Verjovsky, editors, Holomorphic Dynamics. (Proc. Mexico 1986), volume 1345 of Lecture Notes in Math. Springer-Verlag, 1988. MR 89m:57026
5. M. M. Carnicer. The Poincare problem in the non-dicritical case. Annals of Math., 140:289- 294, 1994. MR 95k:32031
6. E. Casas-Alvero. Infinitely near imposed singularities and singularities of polar curves. Math. Ann., 287:429-454, 1990. MR 91h:14002
7. D. Cerveau and A. Lins Neto. Holomorphic foliations in CP(2) having an invariant algebraic curve. Ann. Inst. Fourier, 41(4):883-903, 1991. MR 93b:32050
8. D. Cerveau and J. F. Mattel. Formes integrables holomorphes singulières. Astérisque, 97, 1983. MR 8Gf:58006
9. H. Dulac. Recherches sur les points singuliers des équations différentielles. Journal de l'Ecole Polytechnique, 2e série, 9:1-125, 1904.
10. M.A. Hoskin. Zero-dimensional valuation ideals associated with plane curve branches. Proc. London Math. Soc., 6(3):70-99, 1956. MR 17:665b
11. J. Lipman. Adjoints and polars of simple complete ideals in two dimensional regular local rings. Algebra and geometry week, Tenerife 1992. Bull. Soc. Math. Belg. série A 45(1,2), 1993. MR 97a:13030
12. J. Lipman. Proximity inequalities for complete ideals in two dimensional regular local rings. Contemp. Math., 159, Amer. Math. Soc., Providence, R.I., 1994. MR 95j:13018
13. H. Poincaré. Sur l'intégration algébrique des équations différentielles du premier ordre et du premier degré (I and II). Rendiconti del circolo matematico di Palermo, 5 and 11:161-191 and 193-239, 1891 and 1897.
14. A. Seidenberg. Reduction of singularities of the differentiable equation Ady = Bdi. American Journal of Math., 90:248-269, 1968. MR 36:3762
15. O. Zariski. Studies in equisingularity I. American Journal of Math., 87:507-535, 1965.