Implicitization of surfaces in P³ in the presence of base points

2002/05/31 by Laurent Buse, David Cox, Carlos D'Andrea
Mathematics · #math.AG #math.AC #msc:14Q10 #msc:13D02 #msc:65D17

paper · pdf

published as J. Algebra Appl. 2 (2003), no. 2, 189--214. · 27 pages. Revised version. Accepted for publication in the Journal of Algebra and its Applications

arxiv created 2003/04/29 · arxiv updated 2009/11/30

Abstract

We show that the method of moving quadrics for implicitizing surfaces in P³ 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.

Related

• Equations of Parametric Surfaces with Base Points via Syzygies
• Implicitization of rational surfaces using toric varieties
• A package for computing implicit equations of parametrizations from toric surfaces
• Implicitization of rational ruled surfaces with μ-bases
• Resultants and Moving Surfaces