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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Torsion of the symmetric algebra and implicitization
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by Laurent Busé, Marc Chardin and Jean-Pierre Jouanolou PDF
Proc. Amer. Math. Soc. 137 (2009), 1855-1865 Request permission

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
  • Email: Laurent.Buse@inria.fr
  • Marc Chardin
  • Affiliation: Institut de Mathématiques de Jussieu, CNRS et Université Pierre et Marie Curie, 4 place Jussieu, F-75252 Paris Cedex 05, France
  • MR Author ID: 259215
  • Email: chardin@math.jussieu.fr
  • Jean-Pierre Jouanolou
  • Affiliation: Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg Cedex, France
  • Email: jouanolo@math.u-strasbg.fr
  • 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
  • © Copyright 2009 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 1855-1865
  • MSC (2000): Primary 13C12, 13D25, 13D45, 14E05, 14Q10
  • DOI: https://doi.org/10.1090/S0002-9939-09-09550-1
  • MathSciNet review: 2480264