Torsion of the symmetric algebra and implicitization

Laurent Busé 1 Marc Chardin 2 Jean-Pierre Jouanolou 3
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : Recently, a method to compute the implicit equation of a parametrized hypersurface has been developed by the authors. We address here some questions related to this method. First, we prove that the degree estimate for the stabilization of the MacRae's invariant of a graded part of the symmetric algebra is optimal. Then we show that the extraneous factor that may appear in the process splits into a product a linear forms in the algebraic closure of the base field, each linear form being associated to a non complete intersection base point. Finally, we make a link between this method and a resultant computation for the case of rational plane curves and space surfaces.
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Laurent Busé, Marc Chardin, Jean-Pierre Jouanolou. Torsion of the symmetric algebra and implicitization. Proceedings of the American Mathematical Society, American Mathematical Society, 2009, 137 (6), pp.1855-1865. ⟨inria-00104191v2⟩

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