[Nœuds toriques itérés bidimensionnels et singularités quasi-ordinaires des surfaces]
Nous définissons une notion de nœud torique itéré bidimensionnel, à savoir des plongements particuliers d'un 2-tore dans le produit cartésien d'un 2-tore et d'un 2-disque. Nous appliquons cette définition à la description de la topologie plongée du bord d'un germe quasi-ordinaire irréductible d'hypersurface de dimension 2, en fonction des exposants caractéristiques d'une projection quasi-ordinaire arbitraire. Accessoirement, nous donnons un algorithme de calcul du type de Jung–Hirzebruch de sa normalisation.
We define a notion of 2-dimensional iterated torus knot, namely special embeddings of a 2-torus in the Cartesian product of a 2-torus and a 2-disc. We apply this definition to give a description of the embedded topology of the boundary of an irreducible quasi-ordinary hypersurface germ of dimension 2, in terms of the characteristic exponents of an arbitrary quasi-ordinary projection. Incidentally, we give an algorithm for computing the Jung–Hirzebruch type of its normalization.
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@article{CRMATH_2003__336_8_651_0,
author = {Popescu-Pampu, Patrick},
title = {Two-dimensional iterated torus knots and quasi-ordinary surface singularities},
journal = {Comptes Rendus. Math\'ematique},
pages = {651--656},
publisher = {Elsevier},
volume = {336},
number = {8},
year = {2003},
doi = {10.1016/S1631-073X(03)00099-2},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00099-2/}
}
TY - JOUR AU - Popescu-Pampu, Patrick TI - Two-dimensional iterated torus knots and quasi-ordinary surface singularities JO - Comptes Rendus. Mathématique PY - 2003 SP - 651 EP - 656 VL - 336 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00099-2/ DO - 10.1016/S1631-073X(03)00099-2 LA - en ID - CRMATH_2003__336_8_651_0 ER -
%0 Journal Article %A Popescu-Pampu, Patrick %T Two-dimensional iterated torus knots and quasi-ordinary surface singularities %J Comptes Rendus. Mathématique %D 2003 %P 651-656 %V 336 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00099-2/ %R 10.1016/S1631-073X(03)00099-2 %G en %F CRMATH_2003__336_8_651_0
Popescu-Pampu, Patrick. Two-dimensional iterated torus knots and quasi-ordinary surface singularities. Comptes Rendus. Mathématique, Tome 336 (2003) no. 8, pp. 651-656. doi : 10.1016/S1631-073X(03)00099-2. http://www.numdam.org/articles/10.1016/S1631-073X(03)00099-2/
[1] A Whitney stratification and equisingular family of quasi-ordinary singularities, Proc. Amer. Math. Soc., Volume 117 (1993) no. 2, pp. 305-311
[2] On the link of quasi-ordinary singularities (Aroca, J.M.; Sanchez Giralda, T.; Vicente, J.-L., eds.), Géométrie algébrique et applications II. Singularités et géométrie complexe, Travaux en cours, Vol. 23, Hermann, 1987
[3] Neighborhoods of algebraic sets, Trans. Amer. Math. Soc., Volume 276 (1983) no. 2, pp. 517-530
[4] Introduction to Toric Varieties, Princeton University Press, 1993
[5] Embedded topological classification of quasi-ordinary singularities, Mem. Amer. Math. Soc., Volume 388 (1988)
[6] P. González Pérez, Quasi-ordinary singularities via toric geometry, Thesis, Univ. of La Laguna, Tenerife, Spain, September 2000
[7] Topology of complex singularities (Lê, D.T.; Saito, K.; Teissier, B., eds.), Singularity Theory, World Scientific, 1995
[8] Quasi-ordinary singularities of surfaces in , Part 2, Proc. Sympos. Pure Math., 40, 1983, pp. 161-172
[9] Topological invariants of quasi-ordinary singularities, Mem. Amer. Math. Soc., Volume 388 (1988)
[10] Convex Bodies and Algebraic Geometry: An Introduction to Toric Varieties, Springer-Verlag, 1988
[11] Topological types of quasi-ordinary singularities, Proc. Amer. Math. Soc., Volume 117 (1993) no. 1, pp. 53-59
[12] P. Popescu-Pampu, Arbres de contact des singularités quasi-ordinaires et graphes d'adjacence pour les 3-variétés réelles, Thèse, Univ. Paris 7, novembre 2001
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