Torsion of the symmetric algebra and implicitization

DOI10.1090/S0002-9939-09-09550-1zbMath1167.13008arXivmath/0610186MaRDI QIDQ3629403

Jean-Pierre Jouanolou, Marc Chardin, Laurent Busé

Publication date: 27 May 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610186

zbMATH Keywords

implicitizationRees algebrasymmetric algebra

Mathematics Subject Classification ID

Related Items (16)

A study of a family of monomial ideals ⋮ Strong $\mu$-Bases for Rational Tensor Product Surfaces and Extraneous Factors Associated to Bad Base Points and Anomalies at Infinity ⋮ Fibers of Rational Maps and Elimination Matrices: An Application Oriented Approach ⋮ 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 ⋮ 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 ⋮ Equations defining certain graphs ⋮ The implicitization problem for \(\phi : \mathbb P^n \longrightarrow (\mathbb P^1)^{n+1}\) ⋮ The surface/surface intersection problem by means of matrix based representations ⋮ DEFINING EQUATIONS OF THE REES ALGEBRA OF CERTAIN PARAMETRIC SURFACES ⋮ Fitting ideals and multiple points of surface parameterizations ⋮ Determinantal tensor product surfaces and the method of moving quadrics

Uses Software

• Macaulay2

Cites Work

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• Complete intersections and symmetric algebras
• The dimension and components of symmetric algebras
• On the grade of some ideals
• On the closed image of a rational map and the implicitization problem.
• Invariant aspects of elimination
• The \(\mu \)-basis and implicitization of a rational parametric surface
• Implicitizing rational hypersurfaces using approximation complexes
• Codimension, multiplicity and integral extensions
• IMPLICITIZATION OF SURFACES IN ℙ³ IN THE PRESENCE OF BASE POINTS

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