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Éclatement des coefficients des séries entières et deux théorèmes de Gabrielov

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Abstract

Given a non trivial power series in ℝm × ℝk, it is in general not possible to choose a good direction in ℝk in order to apply Weierstrass Preparation Theorem. Now, one can make it possible by blowing-up coefficients in ℝm. This enables e. g. to prove in some natural way Gabrielov’s complement theorem, as well as Gabrielov’s fiber components theorem in subanalytic geometry.

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Authors and Affiliations

  1. Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4, 30059, Kraków, Poland

    S. Łojasiewicz

  2. IRMAR, Université de Rennes I, Campus de Beaulieu, 35042, Rennes cedex, France

    J. -Cl. Tougeron

  3. Dpto. de Matemáticas, Universidad Autónoma de Madrid, Ciudad Universitaria de Canto Blanco, 28049, Madrid, Spain

    M. -A. Zurro

Authors
  1. S. Łojasiewicz
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  2. J. -Cl. Tougeron
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  3. M. -A. Zurro
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Łojasiewicz, S., Tougeron, J.C. & Zurro, M.A. Éclatement des coefficients des séries entières et deux théorèmes de Gabrielov. Manuscripta Math 92, 325–337 (1997). https://doi.org/10.1007/BF02678197

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  • DOI: https://doi.org/10.1007/BF02678197

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