Desingularizations of plane vector fields
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- by F. Cano PDF
- Trans. Amer. Math. Soc. 296 (1986), 83-93 Request permission
Abstract:
The singularities of a plane vector field can be reduced under quadratic blowing ups. We describe a control method for the singularities of the vector field which works for ground fields of any characteristic and which has no essential obstruction for generalizing to higher dimensional cases.References
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F. Cano, Teoria de distribuciones sobre variedades algebraicas, Colecc. de Mon. del Instituto Jorge Juan, C.S.I.C., Madrid, 1983.
- Jean Giraud, Forme normale d’une fonction sur une surface de caractéristique positive, Bull. Soc. Math. France 111 (1983), no. 2, 109–124 (French, with English summary). MR 734215 —, Condition de Jung pour les revêtements radiciels de hauteur $1$, Proc. Algebraic Geometry, Tokyo/Kyoto 1982, Lecture Notes in Math., vol. 1016, Springer-Verlag, 1983, pp. 313-333. H. Hironaka, Desingularization of excellent surfaces, Advanced Science Seminar in Algebraic Geometry (Summer 1967), Mimeographed notes by B. Benett, Bowdoin College.
- Heisuke Hironaka, Characteristic polyhedra of singularities, J. Math. Kyoto Univ. 7 (1967), 251–293. MR 225779, DOI 10.1215/kjm/1250524227
- A. Seidenberg, Reduction of singularities of the differential equation $A\,dy=B\,dx$, Amer. J. Math. 90 (1968), 248–269. MR 220710, DOI 10.2307/2373435
- Arno van den Essen, Reduction of singularities of the differential equation $Ady=Bdx$, Équations différentielles et systèmes de Pfaff dans le champ complexe (Sem., Inst. Rech. Math. Avancée, Strasbourg, 1975) Lecture Notes in Math., vol. 712, Springer, Berlin, 1979, pp. 44–59. MR 548142
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 296 (1986), 83-93
- MSC: Primary 14D05; Secondary 14B05, 32B30
- DOI: https://doi.org/10.1090/S0002-9947-1986-0837799-3
- MathSciNet review: 837799