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inria-00098684, version 1

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

Laurent Busé ()^a^, 1, 2, David Cox^b^, 3, Carlos D'Andrea^c^, 4

Journal of Algebra and Its Applications 2, 2 (2003) 189--214

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.

a – Université de Nice Sophia-Antipolis
b – Amherst College
c – Universidad de Buenos Aires
1: GALAAD (INRIA Sophia Antipolis)
INRIA – CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS)
2: Laboratoire Jean Alexandre Dieudonné (JAD)
CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS)
3: Department of Mathematics and Computer Science
Amherst College
4: Departamento de Matemática (DM-UBA)
Universidad de Buenos Aires

inria-00098684, version 1
http://hal.inria.fr/inria-00098684
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From: Laurent Busé <>
Submitted on: Monday, 25 September 2006 22:42:11
Updated on: Tuesday, 26 September 2006 09:53:39

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