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Equations of Parametric Surfaces with Base Points via Syzygies

William Adkins·J. William Hoffman·Hao Hao Wang
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Abstract

Let $S$ be a parametric surface in $\proj{3}$ given as the image of $ϕ: \proj{1} \times \proj{1} \to \proj{3}$. 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 $ϕ$ has no base points, and it is an analogous to some of the results of Busé, Cox and D'Andrea for the case when $ϕ: \proj{2} \to \proj{3}$ has base points.

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William Adkins, J. William Hoffman, Hao Hao Wang. 2003-07-24. Equations of Parametric Surfaces with Base Points via Syzygies. https://arxiv.org/abs/math/0306195

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