Details:
Title  Equations of parametric surfaces with base points via syzygies  Author(s)  William A. Adkins, J. William Hoffman, Haohao Wang  Type  Article in Journal  Abstract  Let 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.  Keywords  Parametrization, Implicit equation, Base points, Local complete intersection, Syzygy, Saturation  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717104001221 
Language  English  Journal  Journal of Symbolic Computation  Volume  39  Number  1  Pages  73  101  Year  2005  Edition  0  Translation 
No  Refereed 
No 
