Implicitizing rational hypersurfaces using approximation complexes
We describe an algorithm for implicitizing rational hypersurfaces with at most a finite number of base points, based on a technique described in Buse, Laurent, Jouanolou, Jean-Pierre [2003. On the closed image of a rational map and the implicitization problem. J. Algebra 265, 312-357], where implicit equations are obtained as determinants of certain graded parts of an approximation complex. We detail and improve this method by providing an in-depth study of the cohomology of such a complex. In both particular cases of interest of curve and surface implicitization we also present algorithms which involve only linear algebra routines. (c) 2005 Elsevier Ltd. All rights reserved.
implicitization approximation complexes base points syzygies