The invariance of the algebraic multiplicity of a holomorphic vector field
Rudy Rosas[1]
- [1] Pontificia Universidad Católica del Perú Av Universitaria 1801 San Miguel, Lima 32 (Perú) Instituto de Matemática y Ciencias Afines (IMCA) Jr. los Biólogos 245 La Molina, Lima (Perú)
Annales de l’institut Fourier (2010)
- Volume: 60, Issue: 6, page 2115-2135
- ISSN: 0373-0956
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topRosas, Rudy. "The $C^1$ invariance of the algebraic multiplicity of a holomorphic vector field." Annales de l’institut Fourier 60.6 (2010): 2115-2135. <http://eudml.org/doc/116327>.
@article{Rosas2010,
abstract = {We prove that the algebraic multiplicity of a holomorphic vector field at an isolated singularity is invariant by $C^1$ equivalences.},
affiliation = {Pontificia Universidad Católica del Perú Av Universitaria 1801 San Miguel, Lima 32 (Perú) Instituto de Matemática y Ciencias Afines (IMCA) Jr. los Biólogos 245 La Molina, Lima (Perú)},
author = {Rosas, Rudy},
journal = {Annales de l’institut Fourier},
keywords = {Algebraic multiplicity; holomorphic vector field; holomorphic foliation; algebraic multiplicity},
language = {eng},
number = {6},
pages = {2115-2135},
publisher = {Association des Annales de l’institut Fourier},
title = {The $C^1$ invariance of the algebraic multiplicity of a holomorphic vector field},
url = {http://eudml.org/doc/116327},
volume = {60},
year = {2010},
}
TY - JOUR
AU - Rosas, Rudy
TI - The $C^1$ invariance of the algebraic multiplicity of a holomorphic vector field
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 6
SP - 2115
EP - 2135
AB - We prove that the algebraic multiplicity of a holomorphic vector field at an isolated singularity is invariant by $C^1$ equivalences.
LA - eng
KW - Algebraic multiplicity; holomorphic vector field; holomorphic foliation; algebraic multiplicity
UR - http://eudml.org/doc/116327
ER -
References
top- Bers, L., Riemann surfaces, (1958), New York University Zbl0116.28803
- Burau, W., Kennzeichnung der schlauchknoten, Abh. Math. Sem. Ham. Univ. 9 (1932), 125-133 Zbl0006.03402
- Camacho, C. and Sad, P., Invariant varieties through singularities of holomorphic vector fields, Ann. Math. 115(3) (1982), 579-595 Zbl0503.32007MR657239
- Camacho, C. and Sad, P. and Lins, A., Topological invariants and equidesingularization for holomorphic vector fields, J. Differential Geometry 20 (1984), 143-174 Zbl0576.32020MR772129
- Dieudonné, J., Foundations of modern analysis, enlarged and corrected printing, (1969), Academic Press, New York Zbl0176.00502MR349288
- Dold, A., Lecture notes on algebraic topology, (1972), Springer, Berlin Zbl0234.55001
- Gomez Mont, X. and Seade, J. and Verjovsky, A., The index of a holomorphic flow with an isolated singularity, Math. Ann. 291(4) (1991), 737-751 Zbl0725.32012MR1135541
- Mattei, J.F. and Cerveau, D., Formes intégrables holomorphes singuliéres, (1982), Astérisque 97, Société Mathématique, Paris Zbl0545.32006MR704017
- Mattei, J.F. and Moussu, R., Holonomie et intégrales premiéres, Ann. Sci. École Norm. Sup.(4) 13(4) (1980), 469-523 Zbl0458.32005MR608290
- Milnor, J., Lecture notes on algebraic topology, (1965), University Press of Virginia, Charlottesville
- Pommerenke, Ch., Boundary behaviour of conformal maps, (1992), Springer-Verlag Zbl0762.30001MR1217706
- Rosas, R., On the topological invariance of the algebraic multiplicity of a holomorphic vector field, (2005), Rio de Janeiro
- Rudin, W., Real and complex analysis, (1979), Tata McGraw-Hill, New Delhi Zbl0925.00005
- Taylor, M.E., Partial Differential Equations I, (1996), Springer, New York MR1395148
- Zariski, O., On the topology of algebroid singularities, Amer. Journ. of Math. 54 (1932), 453-465 Zbl58.0614.02MR1507926
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