Implicitization of surfaces in P^3 in the presence of base points

Details Implicitization of surfaces in P^3 in the presence of base points Implicitization of surfaces in P^3 in the presence of base points

2002-05-23

arxiv.org/abs/math/0205251v4

J. Algebra Appl. 2 (2003), no. 2, 189--214.

Mathematics

Algebraic Geometry

27 pages. Revised version. Accepted for publication in the Journal of Algebra and its Applications

Scientific paper

We show that the method of moving quadrics for implicitizing surfaces in P^3
applies in certain cases where base points are present. However, if the ideal
defined by the parametrization is saturated, then this method rarely applies.
Instead, we show that when the base points are a local complete intersection,
the implicit equation can be computed as the resultant of the first syzygies.

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