Reduction of the singularities of foliations and applications

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1. [1] J. M. Aroca, H. Hironaka, J. L. Vicente, The Theory of the Maximal Contact, Memorias de Matemática del Instituto 'Jorge Juan' 29, Madrid, 1975. Zbl0366.32008
2. [2] J. M. Aroca, H. Hironaka, J. L. Vicente, Desingularization Theorems, Memorias de Matemática del Instituto 'Jorge Juan' 30, Madrid, 1975. Zbl0366.32009
3. [3] C. A. Briot, J. C. Bouquet, Propriétés des fonctions définies par les équations différentielles, Journal de l'École Polytechnique 36 (1856), 133-198. 
4. [4] C. Camacho, P. Sad, Invariant varieties through singularities of holomorphic vector fields, Ann. of Math. (2) 115 (1982), 579-595. Zbl0503.32007
5. [5] F. Cano, Dicriticalness of a singular foliation, in: Holomorphic Dynamics (México 1986), X. Gómez-Mont, J. Seade, A. Verjovski (eds.), Lecture Notes in Math. 1345, Springer, Berlin, 1988, 73-94. 
6. [6] F. Cano, Foliaciones singulares dicríticas, Mem. Real Acad. Cienc. Exact. Fís. Natur. Madrid 24 (1989). 
7. [7] F. Cano, Reduction of the singularities of non-dicritical singular foliations. Dimension three, Amer. J. Math. 115 (1993), 509-588. Zbl0786.32023
8. [8] F. Cano, Reduction of singularities of codimension one foliations in dimension three, in preparation, Univ. Valladolid. Zbl1088.32019
9. [9] F. Cano, D. Cerveau, Desingularization of non-dicritical holomorphic foliations and existence of separatrices, Acta Math. 169 (1992), 1-103. Zbl0771.32018
10. [10] F. Cano, J. M. Lion, R. Moussu, Frontière d'une hypersurface pfaffienne, Ann. Sci. École Norm. Sup. (4) 28 (1995), 591-646. Zbl0851.32034
11. [11] F. Cano, J. F. Mattei, Hypersurfaces intégrales des feuilletages holomorphes, Ann. Inst. Fourier (Grenoble) 42 (1992), 49-72. Zbl0762.32018
12. [12] J. Cano, An extension of the Newton-Puiseux polygon construction to give solutions of pfaffian forms, Ann. Inst. Fourier (Grenoble) 43 (1993), 125-142. Zbl0766.34006
13. [13] J. Cano, Construction of invariant curves for holomorphic vector fields, Proc. Amer. Math. Soc. 125 (1997), 2649-2650. Zbl0890.34001
14. [14] V. Cossart, Forme normale pour une fonction sur une variété de dimension trois en caractéristique positive, Thèse d'Etat, Orsay, 1988. 
15. [15] J. Giraud, Forme normale d'une fonction sur une surface de caractéristique positive, Bull. Soc. Math. France 111 (1983), 109-124. Zbl0528.14004
16. [16] J. Giraud, Condition de Jung pour les revêtements radiciels de hauteur un, in: Algebraic Geometry (Tokyo/Kyoto 1982), M. Raynaud and T. Shioda (eds.), Lecture Notes in Math. 1016, Springer, Berlin, 1983, 313-333. 
17. [17] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characterictic zero, Ann. of Math. (2) 79 (1964), 109-203, 205-326. Zbl0122.38603
18. [18] H. Hironaka, Introduction to the Theory of Infinitely Near Singular Points, Memorias de Matemática del Instituto 'Jorge Juan' 28, Madrid, 1975. Zbl0366.32007
19. [19] H. Hironaka, La voûte étoilée, Astérisque 7-8 (1973), 13-20. 
20. [20] H. Hironaka, Idealistic exponents of singularity, in: Algebraic Geometry, John Hopkins Univ. Press, Baltimore, 1977, 52-125. Zbl0496.14011
21. [21] H. Hironaka, Characteristic polyhedra of singularities, J. Math. Kyoto Univ. 7 (1967), 251-293. Zbl0159.50502
22. [22] H. Hironaka, Desingularization of excellent surfaces, appendix in: V. Cossart, J. Giraud, U. Orbanz, Resolution of Surfaces, Lecture Notes in Math. 1101, Springer, Berlin, 1984. 
23. [23] H. Hironaka, Introduction to Real-analytic Sets and Real-analytic Maps, Istituto Matematico L. Tonelli, Pisa, 1973. 
24. [24] H. Hironaka, Subanalytic sets, in: Number Theory, Algebraic Geometry and Commutative Algebra, Kinokuniya, Tokyo, 1973, 453-493. 
25. [25] J. P. Jouanolou, Équations de Pfaff algébriques, Lecture Notes in Math. 708, Springer, Berlin, 1979. 
26. [26] A. G. Khovanskii, Real analytic varieties with the finiteness property and complex abelian integrals, Functional Anal. Appl. 18 (1984), 119-127. 
27. [27] J. M. Lion, Un lemme d'aile pour les ensembles pfaffiens, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), 187-189. Zbl0772.32003
28. [28] S. Łojasiewicz, Ensembles semi-analytiques, Inst. de Hautes Études Scientifiques, Bures-sur-Yvette, 1965. 
29. [29] S. Łojasiewicz, M. A. Zurro, Una introducción a la geometría semi y sub analítica, Secretariado de Publicaciones, Universidad de Valladolid D.L., ed. Serie Ciencias 6, 1993. 
30. [30] B. Malgrange, Frobenius avec singularités. I. Codimension un, Inst. Hautes Études Sci. Publ. Math. 46 (1976), 162-173. Zbl0355.32013
31. [31] J. Martinet, Normalisation des champs de vecteurs holomorphes (d'après A.-D. Bryuno), in: Séminaire Bourbaki, vol. 1980/81, Lecture Notes in Math. 901, Springer, Berlin, 1982, exp. 564, 55-70. 
32. [32] J. F. Mattei, R. Moussu, Holonomie et intégrales premières, Ann. Sci. École Norm. Sup. (4) 13 (1980), 469-523. Zbl0458.32005
33. [33] R. Moussu, C. Roche, Théorie de Hovanskii et problème de Dulac, Invent. Math. 105 (1991), 431-441. Zbl0769.58050
34. [34] R. Moussu, C. Roche, Théorèmes de finitude pour les variétés pfaffiennes, Ann. Inst. Fourier (Grenoble) 42 (1992), 393-420. 
35. [35] A. Seidenberg, Reduction of the singularities of the differential equation Ady=Bdx, Amer. J. Math. 90 (1968), 248-269. Zbl0159.33303
36. [36] Y. T. Siu, Techniques of Extension of Analytic Objects, Lecture Notes in Pure and Appl. Math. 8, Dekker, New York, 1974. Zbl0294.32007
37. [37] M. Spivakovsky, A solution to Hironaka's polyhedra game, in: Arithmetic and Geometry vol. II, M. Artin and J. Tate (eds.), Progr. Math. 36, Birkhäuser, Boston, 1983, 419-432. Zbl0531.14009
38. [38] M. Spivakovsky, Resolution of singularities, preprint, Grenoble-Valladolid-Toronto, 1996.