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]
Rosas, Rudy
Annales de l'Institut Fourier, Tome 60 (2010), p. 2115-2135 / Harvested from Numdam
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On démontre que la multiplicité algébrique d’une singularité d’un champ de vecteurs holomorphe est invariante par C 1 -equivalences.

We prove that the algebraic multiplicity of a holomorphic vector field at an isolated singularity is invariant by C 1 equivalences.

Publié le : 2010-01-01
DOI : https://doi.org/10.5802/aif.2578
Classification:  37F75
Mots clés: multiplicité algébrique, champ de vecteurs holomorphique, feuilletage holomorphique 
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     author = {Rosas, Rudy},
     title = {The $C^1$ invariance of the algebraic multiplicity of a holomorphic vector field},
     journal = {Annales de l'Institut Fourier},
     volume = {60},
     year = {2010},
     pages = {2115-2135},
     doi = {10.5802/aif.2578},
     zbl = {1209.37057},
     mrnumber = {2791652},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2010__60_6_2115_0}
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Rosas, Rudy. The $C^1$ invariance of the algebraic multiplicity of a holomorphic vector field. Annales de l'Institut Fourier, Tome 60 (2010) pp. 2115-2135. doi : 10.5802/aif.2578. http://gdmltest.u-ga.fr/item/AIF_2010__60_6_2115_0/

[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., Tome 9 (1932), pp. 125-133 | Article | Zbl 0006.03402

[3] Camacho, C. And Sad, P. Invariant varieties through singularities of holomorphic vector fields, Ann. Math., Tome 115(3) (1982), pp. 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, Tome 20 (1984), pp. 143-174 | MR 772129 | Zbl 0576.32020

[5] Dieudonné, J. Foundations of modern analysis, enlarged and corrected printing, Academic Press, New York (1969) | MR 349288 | Zbl 0176.00502

[6] Dold, A. Lecture notes on algebraic topology, Springer, Berlin (1972)

[7] Gomez Mont, X. And Seade, J. And Verjovsky, A. The index of a holomorphic flow with an isolated singularity, Math. Ann., Tome 291(4) (1991), pp. 737-751 | MR 1135541 | Zbl 0725.32012

[8] Mattei, J.F. And Cerveau, D. Formes intégrables holomorphes singuliéres, Astérisque 97, Société Mathématique, Paris (1982) | MR 704017 | Zbl 0545.32006

[9] Mattei, J.F. And Moussu, R. Holonomie et intégrales premiéres, Ann. Sci. École Norm. Sup.(4), Tome 13(4) (1980), pp. 469-523 | Numdam | MR 608290 | Zbl 0458.32005

[10] Milnor, J. Lecture notes on algebraic topology, University Press of Virginia, Charlottesville (1965)

[11] Pommerenke, Ch. Boundary behaviour of conformal maps, Springer-Verlag, Grundlehren der Mathematischen Wissenschaften 299, A Series of Comprehensive Studies in Mathematics (1992) | MR 1217706 | Zbl 0762.30001

[12] Rosas, R. On the topological invariance of the algebraic multiplicity of a holomorphic vector field, Rio de Janeiro, IMPA (2005) (Ph. D. Thesis)

[13] Rudin, W. Real and complex analysis, Tata McGraw-Hill, New Delhi (1979) | Zbl 0925.00005

[14] Taylor, M.E. Partial Differential Equations I, Springer, New York (1996) | MR 1395148 | Zbl 0869.35001

[15] Zariski, O. On the topology of algebroid singularities, Amer. Journ. of Math., Tome 54 (1932), pp. 453-465 | Article | JFM 58.0614.02 | MR 1507926 | Zbl 0004.36902