William Adkins, J. William Hoffman, Hao Hao Wang
Published 2003-06-11, updated 2003-07-24Version 2
Let $S$ be a parametric surface in $\proj{3}$ given as the image of $\phi: \proj{1} \times \proj{1} \to \proj{3}$. 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 for when $\phi$ has no base points, and it is an analogous to some of the results of Bus\'{e}, Cox and D'Andrea for the case when $\phi: \proj{2} \to \proj{3}$ has base points.
Comments: 22 pages. Revised version adds proofs that were originally quoted from Hoffman and Wang (arxiv.,org/abs/math.AG/0305125). The paper of Hoffman and Wang has now been withdrawn
Implicitization of surfaces in P^3 in the presence of base points
Implicitization of rational surfaces using toric varieties
On linear systems of P^3 with nine base points
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