581 articles – 596 references  [version française]

inria-00104191, version 1

Complement to the implicitization of rational hypersurfaces by means of approximation complexes

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

Abstract: Recently, a method to compute the implicit equation of a parameterized hypersurface has been developed by the authors. We address here some questions related to this method : optimality of a degree estimate and determination of an extraneous factor that appears when the base points are not locally complete intersections. We then make a link with a resultant computation for the case of rational plane curves and for particular cases of space surfaces. As a consequence, we prove a conjecture of Busé, Cox and D'Andrea.

  • a –  INRIA
  • b –  CNRS
  • c –  Université Louis Pasteur - Strasbourg I
  • 1:  GALAAD (INRIA Sophia Antipolis)
  • INRIA – CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]
  • 2:  Institut de Mathématiques de Jussieu (IMJ)
  • CNRS : UMR7586 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot
  • 3:  Institut de Recherche Mathématique Avancée (IRMA)
  • CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I
  • Domain : Computer Science/Symbolic Computation
    Mathematics/Commutative Algebra
    Mathematics/Algebraic Geometry
  • Available versions :  v1 (2006-10-06) v2 (2007-09-13)
 
  • inria-00104191, version 1
  • http://hal.inria.fr/inria-00104191
  • oai:hal.inria.fr:inria-00104191
  • From: Laurent Busé <>
  • Submitted on: Friday, 6 October 2006 09:31:00
  • Updated on: Friday, 6 October 2006 10:01:01