Residual resultant over the projective plane and the implicitization problem

  • Authors:

  • Laurent Busé

  • Affiliations:

  • UNSA/INRIA, GALAAD, Nice, France

  • Venue:
  • Proceedings of the 2001 international symposium on Symbolic and algebraic computation
  • Year:
  • 2001

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Abstract

In this article, we first generalize the recent notion of residual resultant of a complete intersection [4] to the case of a local complete intersection of codimension 2 in the projective plane, which is the necessary and sufficient condition for a system of three polynomials to have a solution “outside” a variety, defined here by a local complete intersection of codimension 2. We give its degree in the coefficients of each polynomial and compute it as the god of three polynomials or as a product of two determinants divided by another one. In a second part we use this new type of resultant to give a new method to compute the implicit equation of a rational surface with base points in the case where these base points are a local complete intersection of codimension 2.