no. 4
Plane curve singularities and carousels
Tráng, Lê Dung1
1 Université de Provence, CMI, 39 rue Joliot-Curie, 13453 Marseille Cedex 3 (France)
Annales de l'Institut Fourier, Volume 53 (2003) no. 4, pp. 1117-1139.

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.

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.

DOI: 10.5802/aif.1975
Classification: 14J17, 57M27, 57R30
Keywords: plane curve, singularities, carousels, Puiseux expansions, characteristic exponents
Tráng, Lê Dung 1

1 Université de Provence, CMI, 39 rue Joliot-Curie, 13453 Marseille Cedex 3 (France) 
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Tráng, Lê Dung. Plane curve singularities and carousels. Annales de l'Institut Fourier, Volume 53 (2003) no. 4, pp. 1117-1139. doi : 10.5802/aif.1975. https://aif.centre-mersenne.org/articles/10.5802/aif.1975/

[B] K. Brauner Zur Geometrie der Funktionen zweier komplexen Verändlichen III, IV, Abh. Math. Sem. Hamburg, Volume 6 (1928), pp. 8-54

[EN] D. Eisenbud; W. Neumann Three dimensional link theory and invariants of plane curve singularities, Annals of Mathematics Studies, 110, Princeton University Press, Princeton, 1985 | MR | Zbl

[J] W. Jaco Lectures on three-manifold topology (Regional Conference series in Mathematics), Volume 43 (1977) | Zbl

[JS1] W. Jaco; P. Shalen; 3 A new decomposition theorem for irreducible sufficiently large 3-manifolds (Proc. Symp. Pure Math.), Volume 32 (1977), pp. 209-222 | Zbl

[JS2] W. Jaco; P. Shalen Seifert fiber spaces in 3-manifolds, Memoirs A.M.S, Volume 220 (1978) no. 3 | MR | Zbl

[LMW] Lê D.T.; F. Michel; C. Weber 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] Lê D.T.; J. Seade; A. Verjovsky Quadrics, Orthogonal Actions and Involutions in Complex Projective Spaces (to appear in Ens. Math) | Zbl

[Lê1] Lê D.T. Sur les nœuds algébriques, Comp. Math, Volume 25 (1972), pp. 281-321 | Numdam

[Lê2] Lê D.T.; Lê D\ ung Tráng ed. Introduction à la théorie des singularités. Travaux en cours, Volume t. 1-2 (1988), pp. 36-37 | Zbl

[Lê3] Lê D.T. La monodromie n'a pas de point fixe, J. Fac. Sc. Univ. Tokyo, Volume 22 (1975), pp. 409-427 | MR | Zbl

[Lê4] Lê D.T. 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] F. Michel; C. Weber Topologie des germes de courbes planes (1985) (Notes polycopiées)

[P] F. Pham 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] J. Reeve 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] F. Waldhausen Eine Klasse von 3-dimensionaler Mannigfaltigkeiten, Inv. Math, Volume 3 (1967), pp. 87-117 | DOI | MR | Zbl

[Z] O. Zariski Studies in Equisingularity I, Amer. J. Math, Volume 87 (1965), pp. 507-536 | MR | Zbl

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