Quelques calculs utiles pour la résolution des singularitésReport as inadecuate

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1 LMV - Laboratoire de Mathématiques de Versailles 2 IMJ - Institut de Mathématiques de Jussieu

Abstract : This text is the redaction of lectures given in 1971-72 by Monique Lejeune-Jalabert and Bernard Teissier at the Centre de Mathématiques de l-Ecole Polytechnique. The rédaction is due to Lê Dung Tráng and Jean-Jacques Risler. The aim was to give a complete proof of the continuity of maximal contact along the strata of a Samuel stratification in complex analytic geometry. This result is a part of Hironaka-s strategy to prove resolution of singularities in complex analytic geometry. The main ingredients are generalizations of the concept of normal cone of a singular space along a subspace and of the concept of Newton polygon, In particular, we study a generalization of the maximal contact exponent at a singular point of a singular plane curve with a non singular curve through that point. For plane curves, this invariant appears as the inclination of a compact face of the Newton polygon in suitable coordinates, and also as a - critical tropism - for a family of weighted tangent cones.

keyword : Cône normal polygone de Newton contact maximal

Author: Monique Lejeune Jalabert - Bernard Teissier -

Source: https://hal.archives-ouvertes.fr/


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