Quelques Résultats sur Certaines Fonctions à Lieu Singulier de Dimension 1

  • Daniel Barlet
Conference paper
Part of the Trends in Mathematics book series (TM)


This text is a survey on my recent work [B.04] on some holomorphic germs having a one dimensional singular locus. An analogous of the Brieskorn module of an isolated singularity is defined and a finiteness theorem is proved using Kashiwara’s constructibility theorem. A bound for the (finite dimensional) torsion is also obtained. Non existence of torsion is proved for curves (reduced or not) an this property is stable by “Thom-Sebastiani” adjunction of an isolated singularity. This provides a lot of examples in any dimension where our formula r = μ(f)+v(f) generalizing the Milnor number formula, is valid.


Isolate Hypersurface Singularity Holomorphic Germ Suite Exacte Condition Suivante Hyperplane Transverse 
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    Barlet, D. Théorie des (a, b)-modules I, in Complex Analysis and Geometry, Plenum Press, (1993), p. 1–43.Google Scholar
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    Barlet, D. Sur certaines singularités non isolées d’hypersurfaces I, preprint Institut E. Cartan 2004/ n o 03, 47 pages.Google Scholar
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    Barlet, D. and Saito, M. Brieskorn modules and Gauss-Manin systems for non isolated hypersurface singularities, preprint Institut E. Cartan 2004/ n o 54, 16 pages.Google Scholar
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    Kashiwara, M. On the maximally over determined systems of differential equations, Publ. R.I.M.S. vol.10 (1975), p. 563–579.Google Scholar
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    Malgrange, B. Intégrale asymptotique et monodromie, Ann. Sc. Ec. Norm. Sup. 7 (1974), p. 405–430.MathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Daniel Barlet
    • 1
  1. 1.Institut E. Cartan, UMR 7502 CNRS/UHP/INRIAUniversitée H. Poincaré et Institut Universitaire de FranceVandoeuvre-les-NancyFrance

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