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On Zariski's multiplicity problem

Authors: Georges Comte, Pierre Milman and David Trotman
Journal: Proc. Amer. Math. Soc. 130 (2002), 2045-2048
MSC (2000): Primary 32S15, 32S25; Secondary 32S50, 57N99, 58K15
Published electronically: January 23, 2002
MathSciNet review: 1896040
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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.

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Additional Information

Georges Comte
Affiliation: Laboratoire J. Dieudonné, UMR CNRS 6621, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice, France

Pierre Milman
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3

David Trotman
Affiliation: Laboratoire d’Analyse, Topologie et Probabilités, UMR CNRS 6632, Université de Provence, 39, rue Joliot-Curie, 13453 Marseille, France

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
Published electronically: January 23, 2002
Communicated by: Paul Goerss
Article copyright: © Copyright 2002 American Mathematical Society