Torsion of the symmetric algebra and implicitization
| Autor: | Laurent Busé, Marc Chardin, Jean Pierre Jouanolou |
|---|---|
| Přispěvatelé: | Geometry, algebra, algorithms (GALAAD), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Jussieu (IMJ), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (1965 - 2019) (UNS) |
| Rok vydání: | 2006 |
| Předmět: |
13D02
13D25 Plane curve General Mathematics [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC] Complete intersection 02 engineering and technology Commutative Algebra (math.AC) 01 natural sciences Algebraic closure Mathematics - Algebraic Geometry 13A30 13D30 14Q10 Linear form 0202 electrical engineering electronic engineering information engineering FOS: Mathematics 0101 mathematics Invariant (mathematics) Algebraic Geometry (math.AG) Mathematics Symmetric algebra [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC] Applied Mathematics 010102 general mathematics 020207 software engineering Mathematics - Commutative Algebra Algebra Hypersurface Torsion (algebra) [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] |
| Zdroj: | Proceedings of the American Mathematical Society Proceedings of the American Mathematical Society, American Mathematical Society, 2009, 137 (6), pp.1855-1865 Proceedings of the American Mathematical Society, 2009, 137 (6), pp.1855-1865 |
| ISSN: | 0002-9939 1088-6826 |
| DOI: | 10.48550/arxiv.math/0610186 |
| Popis: | Recently, a method to compute the implicit equation of a parametrized hypersurface has been developed by the authors. We address here some questions related to this method. First, we prove that the degree estimate for the stabilization of the MacRae’s invariant of Sym A ( I ) ν \operatorname {Sym}_{A}(I)_{\nu } is optimal. Then, we show that the extraneous factor that may appear in the process splits into a product of linear forms in the algebraic closure of the base field, each linear form being associated to a non-complete intersection base point. Finally, we make a link between this method and a resultant computation for the case of rational plane curves and space surfaces. |
| Databáze: | OpenAIRE |
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