Implicitization of surfaces in the projective space in the presence of base points

Laurent Busé 1, 2 David Cox 3 Carlos d'Andrea 4
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We show that the method of moving quadrics for implicitizing surfaces in $\PP^3$ 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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Laurent Busé, David Cox, Carlos d'Andrea. Implicitization of surfaces in the projective space in the presence of base points. Journal of Algebra and Its Applications, World Scientific Publishing, 2003, 2 (2), pp.189--214. ⟨inria-00098684⟩

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