IMPLICITIZATION OF SURFACES IN ℙ3 IN THE PRESENCE OF BASE POINTS-Reference-Cited by-同舟云学术

IMPLICITIZATION OF SURFACES IN ℙ3 IN THE PRESENCE OF BASE POINTS

Published:2003-06 Issue:02 Volume:02 Page:189-214
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

BUSÉ LAURENT¹,COX DAVID²,D'ANDREA CARLOS³

Affiliation:

1. UNSA, UMR 6621, Parc Valrose, BP 71, 06108 Nice Cedex 02, France

2. Department of Mathematics and Computer Science, Amherst College, Amherst, MA 01002-5000, USA

3. Miller Instifute for Basic Research in Science and Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720-3840, USA

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498803000489

Reference22 articles.

1. Resultant over the residual of a complete intersection

2. D. Bayer and D. Mumford, Computational Algebraic Geometry and Commutative Algebra (Cambridge Univ. Press, Cambridge, 1993) pp. 1–48.

3. A criterion for detectingm-regularity

Cited by 62 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Computing the intersection between a rational parametric curve and a rational parametric surface;Computer Aided Geometric Design;2024-03

2. Topology Guaranteed B-Spline Surface/Surface Intersection;ACM Transactions on Graphics;2023-12-05

3. An Algorithm to Compute the $$\mu $$-Bases of Rational Parametric Surfaces with Respect to One Variable;Communications in Mathematics and Statistics;2023-02-13

4. Implicit Representations of Rational Curves and Surfaces;SISSA Springer Series;2022-12-24

5. Computing the Intersection of Two Rational Surfaces Using Matrix Representations;Computer-Aided Design;2022-09