Moving curve ideals of rational plane parametrizations

Abstract

In the nineties, several methods for dealing in a more efficient way with the implicitization of rational parametrizations were explored in the Computer Aided Geometric Design Community. The analysis of the validity of these techniques has been a fruitful ground for Commutative Algebraists and Algebraic Geometers, and several results have been obtained so far. Yet, a lot of research is still being done currently around this topic. In this note we present these methods, show their mathematical formulation, and survey current results and open questions.

16 pages, 8 figures. Revised version of a survey to appear in the LNCS proceedings of the workshop "Computer Algebra and Polynomials" (Linz, November 2013)

References in corpus (3)

• The bi-graded structure of Symmetric Algebras with applications to Rees rings
• Implicitization of de Jonquières parametrizations
• Strata of vector spaces of forms in k[x,y] and of rational curves in P^k