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Rudy Rosas
The $C^1$ invariance of the algebraic multiplicity of a holomorphic vector field
(La $C^1$-invariance de la multiplicité algébrique d’un champ de vecteurs holomorpe)
Annales de l'institut Fourier, 60 no. 6 (2010), p. 2115-2135, doi: 10.5802/aif.2578
Article: subscription required (your ip address: 50.16.108.167) | Reviews MR 2791652
Class. Math.: 37F75
Keywords: Algebraic multiplicity, holomorphic vector field, holomorphic foliation
[1] Bers, L., Riemann surfaces, New York University, 1958, Notes by Richard Pollack and James Radlow
[2] Burau, W., “Kennzeichnung der schlauchknoten”, Abh. Math. Sem. Ham. Univ. 9 (1932), p. 125-133
Article | Zbl 0006.03402
[3] Camacho, C. and Sad, P., “Invariant varieties through singularities of holomorphic vector fields”, Ann. Math. 115(3) (1982), p. 579-595
Article | MR 657239 | Zbl 0503.32007
[4] Camacho, C. and Sad, P. and Lins, A., “Topological invariants and equidesingularization for holomorphic vector fields”, J. Differential Geometry 20 (1984), p. 143-174
Article | MR 772129 | Zbl 0576.32020
[5] Dieudonné, J., Foundations of modern analysis, enlarged and corrected printing, Academic Press, 1969 MR 349288 | Zbl 0176.00502
[6] Dold, A., Lecture notes on algebraic topology, Springer, 1972
[7] Gomez Mont, X. and Seade, J. and Verjovsky, A., “The index of a holomorphic flow with an isolated singularity”, Math. Ann. 291(4) (1991), p. 737-751 MR 1135541 | Zbl 0725.32012
[8] Mattei, J.F. and Cerveau, D., Formes intégrables holomorphes singuliéres, Astérisque 97, Société Mathématique, 1982 MR 704017 | Zbl 0545.32006
[9] Mattei, J.F. and Moussu, R., “Holonomie et intégrales premiéres”, Ann. Sci. École Norm. Sup.(4) 13(4) (1980), p. 469-523
Numdam | MR 608290 | Zbl 0458.32005
[10] Milnor, J., Lecture notes on algebraic topology, University Press of Virginia, 1965
[11] Pommerenke, Ch., Boundary behaviour of conformal maps, Grundlehren der Mathematischen Wissenschaften 299, A Series of Comprehensive Studies in Mathematics, Springer-Verlag, 1992 MR 1217706 | Zbl 0762.30001
[12] Rosas, R., On the topological invariance of the algebraic multiplicity of a holomorphic vector field, thesis, IMPA, 2005
[13] Rudin, W., Real and complex analysis, Tata McGraw-Hill, 1979 Zbl 0925.00005
[14] Taylor, M.E., Partial Differential Equations I, Springer, 1996 MR 1395148
[15] Zariski, O., “On the topology of algebroid singularities”, Amer. Journ. of Math. 54 (1932), p. 453-465
Article | MR 1507926 | JFM 58.0614.02
Rudy Rosas
The $C^1$ invariance of the algebraic multiplicity of a holomorphic vector field
(La $C^1$-invariance de la multiplicité algébrique d’un champ de vecteurs holomorpe)
Annales de l'institut Fourier, 60 no. 6 (2010), p. 2115-2135, doi: 10.5802/aif.2578
Article: subscription required (your ip address: 50.16.108.167) | Reviews MR 2791652
Class. Math.: 37F75
Keywords: Algebraic multiplicity, holomorphic vector field, holomorphic foliation
Résumé - Abstract
We prove that the algebraic multiplicity of a holomorphic vector field at an isolated singularity is invariant by $C^1$ equivalences.
Bibliography
[2] Burau, W., “Kennzeichnung der schlauchknoten”, Abh. Math. Sem. Ham. Univ. 9 (1932), p. 125-133
Article | Zbl 0006.03402
[3] Camacho, C. and Sad, P., “Invariant varieties through singularities of holomorphic vector fields”, Ann. Math. 115(3) (1982), p. 579-595
Article | MR 657239 | Zbl 0503.32007
[4] Camacho, C. and Sad, P. and Lins, A., “Topological invariants and equidesingularization for holomorphic vector fields”, J. Differential Geometry 20 (1984), p. 143-174
Article | MR 772129 | Zbl 0576.32020
[5] Dieudonné, J., Foundations of modern analysis, enlarged and corrected printing, Academic Press, 1969 MR 349288 | Zbl 0176.00502
[6] Dold, A., Lecture notes on algebraic topology, Springer, 1972
[7] Gomez Mont, X. and Seade, J. and Verjovsky, A., “The index of a holomorphic flow with an isolated singularity”, Math. Ann. 291(4) (1991), p. 737-751 MR 1135541 | Zbl 0725.32012
[8] Mattei, J.F. and Cerveau, D., Formes intégrables holomorphes singuliéres, Astérisque 97, Société Mathématique, 1982 MR 704017 | Zbl 0545.32006
[9] Mattei, J.F. and Moussu, R., “Holonomie et intégrales premiéres”, Ann. Sci. École Norm. Sup.(4) 13(4) (1980), p. 469-523
Numdam | MR 608290 | Zbl 0458.32005
[10] Milnor, J., Lecture notes on algebraic topology, University Press of Virginia, 1965
[11] Pommerenke, Ch., Boundary behaviour of conformal maps, Grundlehren der Mathematischen Wissenschaften 299, A Series of Comprehensive Studies in Mathematics, Springer-Verlag, 1992 MR 1217706 | Zbl 0762.30001
[12] Rosas, R., On the topological invariance of the algebraic multiplicity of a holomorphic vector field, thesis, IMPA, 2005
[13] Rudin, W., Real and complex analysis, Tata McGraw-Hill, 1979 Zbl 0925.00005
[14] Taylor, M.E., Partial Differential Equations I, Springer, 1996 MR 1395148
[15] Zariski, O., “On the topology of algebroid singularities”, Amer. Journ. of Math. 54 (1932), p. 453-465
Article | MR 1507926 | JFM 58.0614.02
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