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Étude du résultant sur une variété algébrique

Laurent Busé 1, 2 
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In this thesis a theoric and practical study of residual resultant is proposed. This residual resultant provides a necessary and sufficient condition so that an algebraic system has solutions on a residual variety obtained by blowing-up. Effective methods to compute this residual resultant as its degree are exposed, more precise results being obtained when the locus that one blows up is a complete intersection or a projective local complete intersection Cohen-Macaulay of codimension two. An algorithm to solve the implicitization problem in case the parametrization has base points which are a local complete intersection is proposed using residual resultant. One also shows how this residual resultant allows to obtain the Chow form of the isolated points of an algebraic system. Finally the last chapter of this thesis gives a definition and a first study of determinantal resultant which traduces a necessary and sufficient condition so that a generic matrix is of rank less or equal to a given positive integer.
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Submitted on : Wednesday, September 20, 2006 - 1:11:29 PM
Last modification on : Thursday, August 4, 2022 - 5:05:34 PM
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  • HAL Id : tel-00096815, version 1



Laurent Busé. Étude du résultant sur une variété algébrique. Mathématiques [math]. Université Nice Sophia Antipolis, 2001. Français. ⟨NNT : ⟩. ⟨tel-00096815⟩



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