Table of contents

  • This session has been presented December 12, 2003.

Description

  • Speaker

    Claude Quitté - Université de Poitiers

Après avoir traité un exemple élémentaire (multiplicité d'un point sur une courbe plane ou plus généralement d'une hypersurface), nous fournissons la définition du polynôme et de la série d'Hilbert-Samuel d'un anneau local noethérien. Nous considérerons également le cadre gradué, cadre dans lequel le polynôme d'Hilbert-Samuel (ou la série) permet en particulier le calcul de la dimension (de Krull). Nous tenterons de faire le lien entre les deux cadres (local, gradué) via l'anneau gradué associé à un anneau local ce qui conduit d'un point de vue géométrique à la notion de cône tangent.<br/> Il est prévu de traiter quelques exemples élémentaires. Un algorithme de calcul de la série d'Hilbert-Samuel d'un idéal homogène à l'aide des bases de Groebner sera donné.

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