IMPLICITIZATION OF SURFACES IN ℙ3 IN THE PRESENCE OF BASE POINTS
From MaRDI portal
Publication:4474464
DOI10.1142/S0219498803000489zbMath1068.14066arXivmath/0205251MaRDI QIDQ4474464
Carlos D'Andrea, David A. Cox, Laurent Busé
Publication date: 12 July 2004
Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0205251
Computer science aspects of computer-aided design (68U07) Computational aspects of algebraic surfaces (14Q10) Syzygies, resolutions, complexes and commutative rings (13D02) Hypersurfaces and algebraic geometry (14J70)
Related Items (42)
Algorithms for computing strong \(\mu\)-bases for rational tensor product surfaces ⋮ A study of a family of monomial ideals ⋮ Implicitizing rational surfaces using moving quadrics constructed from moving planes ⋮ An improved algorithm for constructing moving quadrics from moving planes ⋮ Strong $\mu$-Bases for Rational Tensor Product Surfaces and Extraneous Factors Associated to Bad Base Points and Anomalies at Infinity ⋮ Almost-toric hypersurfaces ⋮ Fibers of Rational Maps and Elimination Matrices: An Application Oriented Approach ⋮ Implicitization of parametric curves via Lagrange interpolation ⋮ A simple method for implicitizing rational curves and surfaces ⋮ A matrix-based approach to properness and inversion problems for rational surfaces ⋮ A Note on Quadratically Parametrized Surfaces ⋮ Survey on the theory and applications of \(\mu\)-bases for rational curves and surfaces ⋮ A constructive approach to implicitizing rational surfaces with LCI base points by moving planes and moving quadrics ⋮ Bound for the number of one-dimensional fibers of a projective morphism ⋮ Elimination and nonlinear equations of Rees algebras ⋮ The implicit equation of a multigraded hypersurface ⋮ Computing the intersection between a rational parametric curve and a rational parametric surface ⋮ Implicitization, parameterization and singularity computation of Steiner surfaces using moving surfaces ⋮ Matrix representations for toric parametrizations ⋮ Implicitization of rational hypersurfaces via linear syzygies: a practical overview ⋮ Compactifications of rational maps, and the implicit equations of their images ⋮ Minimal generators of the defining ideal of the Rees algebra associated to monoid parameterizations ⋮ A partial solution to the problem of proper reparametrization for rational surfaces ⋮ Computing the form of highest degree of the implicit equation of a rational surface ⋮ Fibers of Multi-Graded Rational Maps and Orthogonal Projection onto Rational Surfaces ⋮ Equations of parametric surfaces with base points via syzygies ⋮ The \(\mu \)-basis and implicitization of a rational parametric surface ⋮ Implicitizing rational hypersurfaces using approximation complexes ⋮ Residue calculus and applications ⋮ Computation of the singularities of parametric plane curves ⋮ A univariate resultant-based implicitization algorithm for surfaces ⋮ Behavior of the fiber and the base points of parametrizations under projections ⋮ On the homology of two-dimensional elimination ⋮ The surface/surface intersection problem by means of matrix based representations ⋮ On the problem of proper reparametrization for rational curves and surfaces ⋮ ON THE IRREDUCIBILITY OF THE DETERMINANT OF THE MATRIX OF MOVING PLANES ⋮ Implicitization of rational surfaces using toric varieties ⋮ Some Results on the Surjectivity of Surface Parametrizations ⋮ Torsion of the symmetric algebra and implicitization ⋮ Determinantal tensor product surfaces and the method of moving quadrics ⋮ Implicitizing rational surfaces without base points by moving planes and moving quadrics ⋮ On the base point locus of surface parametrizations: formulas and consequences
Cites Work
- A criterion for detecting m-regularity
- Generalised characteristic polynomials
- Algorithm for implicitizing rational parametric surfaces
- The moving line ideal basis of planar rational curves
- Multigraded resultants of Sylvester type
- On the validity of implicitization by moving quadrics for rational surfaces with no base points
- Regularity of the powers of an ideal
- Local complete intersections in $\mathbb {P}^2$ and Koszul syzygies
- What can be computed in algebraic geometry?
- Resultants and moving surfaces
- The \(\mu\)-basis of a rational ruled surface
- Resultant over the residual of a complete intersection.
- Explicit formulas for the multivariate resultant.
This page was built for publication: IMPLICITIZATION OF SURFACES IN ℙ3 IN THE PRESENCE OF BASE POINTS