Equations of Parametric Surfaces with Base Points via Syzygies

Details Equations of Parametric Surfaces with Base Points via Syzygies Equations of Parametric Surfaces with Base Points via Syzygies

2003-06-11

arxiv.org/abs/math/0306195v2

Mathematics

Algebraic Geometry

22 pages. Revised version adds proofs that were originally quoted from Hoffman and Wang (arxiv.,org/abs/math.AG/0305125). The

Scientific paper

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.

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