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Torsion of the symmetric algebra and implicitization

Authors: Laurent Busé, Marc Chardin and Jean-Pierre Jouanolou
Journal: Proc. Amer. Math. Soc. 137 (2009), 1855-1865
MSC (2000): Primary 13C12, 13D25, 13D45, 14E05, 14Q10
Published electronically: February 4, 2009
MathSciNet review: 2480264
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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 $ \operatorname{Sym}_{A}(I)_{\nu}$ is optimal. Then, we show that the extraneous factor that may appear in the process splits into a product of 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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Additional Information

Laurent Busé
Affiliation: Galaad, INRIA, 2004 route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex, France

Marc Chardin
Affiliation: Institut de Mathématiques de Jussieu, CNRS et Université Pierre et Marie Curie, 4 place Jussieu, F-75252 Paris Cedex 05, France

Jean-Pierre Jouanolou
Affiliation: Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg Cedex, France

Keywords: Implicitization, symmetric algebras, Rees algebras.
Received by editor(s): October 5, 2006
Received by editor(s) in revised form: September 13, 2007, and February 5, 2008
Published electronically: February 4, 2009
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2009 American Mathematical Society

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