Dans cet article nous donnons une description directe et explicite du plongement topologique local d'une singularité de courbe plane à partir des dévelopements de Puiseux de ses branches relativement à un système de coordonnées fixé.
In this paper we give a direct and explicit description of the local topological embedding of a plane curve singularity using the Puiseux expansions of its branches in a given set of coordinates.
Keywords: plane curve, singularities, carousels, Puiseux expansions, characteristic exponents
Mot clés : courbe plane, singularités, carrousels, expansions de Puiseux, exposants caractéristiques
@article{AIF_2003__53_4_1117_0, author = {Tr\'ang, L\^e Dung}, title = {Plane curve singularities and carousels}, journal = {Annales de l'Institut Fourier}, pages = {1117--1139}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {4}, year = {2003}, doi = {10.5802/aif.1975}, mrnumber = {2033511}, zbl = {1078.14050}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1975/} }
TY - JOUR AU - Tráng, Lê Dung TI - Plane curve singularities and carousels JO - Annales de l'Institut Fourier PY - 2003 SP - 1117 EP - 1139 VL - 53 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1975/ DO - 10.5802/aif.1975 LA - en ID - AIF_2003__53_4_1117_0 ER -
Tráng, Lê Dung. Plane curve singularities and carousels. Annales de l'Institut Fourier, Tome 53 (2003) no. 4, pp. 1117-1139. doi : 10.5802/aif.1975. http://www.numdam.org/articles/10.5802/aif.1975/
[B] Zur Geometrie der Funktionen zweier komplexen Verändlichen III, IV, Abh. Math. Sem. Hamburg, Volume 6 (1928), pp. 8-54
[EN] Three dimensional link theory and invariants of plane curve singularities, Annals of Mathematics Studies, 110, Princeton University Press, Princeton, 1985 | MR | Zbl
[J] Lectures on three-manifold topology (Regional Conference series in Mathematics), Volume 43 (1977) | Zbl
[JS1] A new decomposition theorem for irreducible sufficiently large 3-manifolds (Proc. Symp. Pure Math.), Volume 32 (1977), pp. 209-222 | Zbl
[JS2] Seifert fiber spaces in 3-manifolds, Memoirs A.M.S, Volume 220 (1978) no. 3 | MR | Zbl
[LMW] Sur le comportement des polaires associées aux germes de courbes planes, Ann. Ec. Norm. Sup., 4ème Série, Volume 24 (1991), pp. 141-169 | Numdam | MR | Zbl
[LSV] Quadrics, Orthogonal Actions and Involutions in Complex Projective Spaces (to appear in Ens. Math) | Zbl
[Lê1] Sur les nœuds algébriques, Comp. Math, Volume 25 (1972), pp. 281-321 | Numdam
[Lê2] Introduction à la théorie des singularités. Travaux en cours, Volume t. 1-2 (1988), pp. 36-37 | Zbl
[Lê3] La monodromie n'a pas de point fixe, J. Fac. Sc. Univ. Tokyo, Volume 22 (1975), pp. 409-427 | MR | Zbl
[Lê4] The geometry of the monodromy theorem, C. P. Ramanujam, a tribute (Tata Inst. Fund. Res. Studies in Math), Volume 8 (1978), pp. 157-173 | Zbl
[MW] Topologie des germes de courbes planes (1985) (Notes polycopiées)
[P] Singularités des courbes planes (1972) (Cours à l'université Paris 7, rédigé par J.L. Dupeyrat, Notes miméographiées, Centre de Mathématiques, École Polytechnique) | MR | Zbl
[R] A summary of results in the topological classification of plane algebroid singularities, Rendiconti Sem. Mat. Torino, Volume 14 (1954--55), pp. 159-187 | MR | Zbl
[W] Eine Klasse von 3-dimensionaler Mannigfaltigkeiten, Inv. Math, Volume 3 (1967), pp. 87-117 | DOI | MR | Zbl
[Z] Studies in Equisingularity I, Amer. J. Math, Volume 87 (1965), pp. 507-536 | MR | Zbl
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