Torsion of the symmetric algebra and implicitization
Commutative Algebra
2007-09-13 v2 Algebraic Geometry
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.
Cite
@article{arxiv.math/0610186,
title = {Torsion of the symmetric algebra and implicitization},
author = {Laurent Buse and Marc Chardin and Jean-Pierre Jouanolou},
journal= {arXiv preprint arXiv:math/0610186},
year = {2007}
}