Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

On Zariski's multiplicity problem

Author(s): Georges Comte; Pierre Milman; David Trotman
Journal: Proc. Amer. Math. Soc. 130 (2002), 2045-2048.
MSC (2000): Primary 32S15, 32S25; Secondary 32S50, 57N99, 58K15
Posted: January 23, 2002
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We show that to answer affirmatively Zariski's question concerning the topological invariance of the multiplicity of complex analytic hypersurfaces at isolated singular points, it suffices to prove two combined statements, each of which may be obtained separately.

References:

[Co]
G. Comte, Multiplicity of complex analytic sets and bilipschitz maps, Real analytic and algebraic singularities, Pitman Research Notes in Mathematics Series 381 (T. Fukuda, T. Fukui, S. Izumiya, S. Koike, eds.), (1998), 182-188. MR 99a:32048

[Ka]
U. Karras, Equimultiplicity of deformations of constant Milnor number, Proceedings of the Conference on Algebraic Geometry, Berlin 1985, Teubner-texte zur Mathematik, Band 92 (H. Kurke, M. Roczen, eds.), (1986), 186-209. MR 89f:32012

[Ki]
H. King, Topological type of isolated critical points, Annals of Math. 107 (1978), 385-397. MR 58:13081

[KS1]
R. Kirby and L. C. Siebenmann, Normal bundles for codimension 2 locally flat embeddings, Geometric topology (Proc. Conf., Park City, Utah, 1974, edited by L. C. Glaser and T. B. Rushing), Lecture Notes in Math. 438, Berlin-Heidelberg-New York, Springer (1975), 310-324. MR 53:4072

[KS2]
R. Kirby and L. C. Siebenmann, Foundational essays on topological manifolds, Annals of Math. Studies no. 88, Princeton University Press (1977). MR 58:31082

[Mi]
J. Milnor, Singular points of complex hypersurfaces, Annals of Math. Studies no. 61, Princeton University Press (1968). MR 39:969

[Mo]
T. Mostowski, Lipschitz equisingularity, Dissertationes Math. 243 (1985). MR 87e:32008

[Pe]
B. Perron, Conjugaison topologique des germes de fonctions holomorphes à singularité isolée en dimension trois, Invent. Math. 82 (1985), 27-35. MR 87d:32011

[Pl]
A. P\loski, Multiplicity and the \Lojasiewicz exponent, Singularities (Warsaw, 1985), Banach Center Publications 20, PWN, Warsaw, (1988), 353-364. MR 92d:32049

[Q]
F. Quinn, Ends of maps, III; dimension 4 and 5, J. Diff. Geom. 17 (1982), 503-521. MR 84j:57012

[Ri-Tr]
J.-J. Risler, D. Trotman, Bilipschitz invariance of the multiplicity, Bull. London. Math. Soc. 29 (1997), 200-204. MR 97i:32049

[Sa]
O. Saeki, Topological types of complex isolated hypersurface singularities, Kodai Math. J. 12 (1989), 23-29. MR 90c:32012

[Te]
B. Teissier, A bouquet of bouquets for a birthday, Topological methods in modern mathematics (Stony Brook, NY, 1991), Publish or Perish, Houston, Texas (1993), 93-122. MR 94b:32062

[Tr]
D. Trotman, Partial results on the topological invariance of the multiplicity of a complex hypersurface, Séminaire A'Campo-MacPherson, Univ. Paris 7, 1977, Thèse d'Etat, Orsay, January 1980.

[W]
C. T. C. Wall, Surgery on compact manifolds, Academic Press, New York (1970). MR 55:4217

[Za]
O. Zariski, Some open questions in the theory of singularities, Bull. Amer. Math. Soc. 77 (1971), 481-491. MR 43:3266

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32S15, 32S25, 32S50, 57N99, 58K15

Retrieve articles in all Journals with MSC (2000): 32S15, 32S25, 32S50, 57N99, 58K15

Additional Information:

Georges Comte
Affiliation: Laboratoire J. Dieudonné, UMR CNRS 6621, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice, France
Email: comte@math.unice.fr

Pierre Milman
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email: milman@math.toronto.edu

David Trotman
Affiliation: Laboratoire d'Analyse, Topologie et Probabilités, UMR CNRS 6632, Université de Provence, 39, rue Joliot-Curie, 13453 Marseille, France
Email: trotman@gyptis.univ-mrs.fr

DOI: 10.1090/S0002-9939-02-06430-4
PII: S 0002-9939(02)06430-4
Keywords: Multiplicity, topological type, complex hypersurface, singular point
Received by editor(s): January 14, 2000
Received by editor(s) in revised form: February 1, 2001
Posted: January 23, 2002
Communicated by: Paul Goerss
Copyright of article: Copyright 2002, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google