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Invariants d'une désingularisation et singularités des morphismes

Published online by Cambridge University Press:  04 December 2007

Benoît Audoubert ,
Fouad El Zein  and
Lê Dũng Tráng
Benoît Audoubert
Affiliation:
Department of Mathematics, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlandsbaudou@math.metro-u.ac.jp Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan
Fouad El Zein
Affiliation:
Département de Mathématiques, Université de Provence, 2, rue de la Houssinière, 44 322 Nantes cedex 03, Franceelzein@math.univ-nantes.fr
Lê Dũng Tráng
Affiliation:
Centre de Mathématiques, Université de Provence, 39, rue F. Joliot Curie, 13 453 Marseille cedex 13, Franceledt@gyptis.univ-mrs.fr
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Abstract

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Let (X, 0) be a germ of an analytic space and f the germ of an analytic function on X. We show that the polar filtration of the local Milnor fiber, defined by a projection on a complex disc, is diffeomorphic to a valuative filtration of the Milnor fiber called Hironaka's filtration, a result which links invariants associated with the singularities of the projection to those associated with a desingularisation.

Keywords

singularitieslocal Milnor fiberpolar constructionresolution of singularities14B0532S0532S55
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 4 , July 2004 , pp. 993 - 1010
Copyright
Foundation Compositio Mathematica 2004