inria-00104191, version 2

Torsion of the symmetric algebra and implicitization

Laurent Busé () ^a, 1, Marc Chardin ^b, 2, Jean-Pierre Jouanolou ³

Proceedings of the American Mathematical Society 137, 6 (2009) 1855-1865

• a –  INRIA
• b –  CNRS
• 1:  GALAAD (INRIA Sophia Antipolis)
• 
  INRIA – CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS] France
• 2:  Institut de Mathématiques de Jussieu (IMJ)
• http://www.institut.math.jussieu.fr/
  CNRS : UMR7586 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot 2, place Jussieu 75251 Paris Cedex 05 France
• 3:  Institut de Recherche Mathématique Avancée (IRMA)
• http://www-irma.u-strasbg.fr/
  CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I 7 rue René-Descartes, 67084 Strasbourg Cedex, France France

Available versions :  v1 (2006-10-06) v2 (2007-09-13)

Bibliographic reference

• Type of document: Articles in peer-reviewed journal
• Domain:

  Computer Science/Symbolic Computation

  Mathematics/Commutative Algebra

  Mathematics/Algebraic Geometry

• Title: Torsion of the symmetric algebra and implicitization
• 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.
• Full text language: English
• Journal title:

  Proceedings of the American Mathematical Society
  Publisher	American Mathematical Society
  ISSN	0002-9939

• Publication date: 2009
• Audience: international
• Commercial editor: American Mathematical Society
• Volume: 137
• Number: 6
• Pagination: 1855-1865

Attached file list to this document: 

• inria-00104191, version 2
• http://hal.inria.fr/inria-00104191
• oai:hal.inria.fr:inria-00104191
• From: Laurent Busé <>
• Submitted on: Thursday, 13 September 2007 11:29:01
• Updated on: Wednesday, 3 March 2010 15:08:52