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TitleEquations of parametric surfaces with base points via syzygies
Author(s) William A. Adkins, J. William Hoffman, Haohao Wang
TypeArticle in Journal
AbstractLet S be a tensor product parametrized surface in P^3 ; that is, S is given as the image of φ : P^1 × P^1 → P^3 . This paper will show that the use of syzygies in the form of a combination of moving planes and moving quadrics provides a valid method for finding the implicit equation of S when certain base points are present. This work extends the algorithm provided by Cox [Cox, D.A., 2001. Equations of parametric curves and surfaces via syzygies. In: Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering. Contemporary Mathematics vol. 286, pp. 1–20] for when φ has no base points, and it is analogous to some of the results of Busé et al. [Busé, L., Cox, D., D’Andrea, C., 2003. Implicitization of surfaces in P 3 in the presence of base points. J. Algebra Appl. 2 (2), 189–214] for the case of a triangular parametrization φ : P^2 → P^3 with base points.
KeywordsParametrization, Implicit equation, Base points, Local complete intersection, Syzygy, Saturation
URL http://www.sciencedirect.com/science/article/pii/S0747717104001221
JournalJournal of Symbolic Computation
Pages73 - 101
Translation No
Refereed No