HAL - INRIA :: [inria-00104191, version 2] Torsion of the symmetric algebra and implicitization

inria-00104191, version 2

Torsion of the symmetric algebra and implicitization

Laurent Busé ()^a^, 1, Marc Chardin^b^, 2, Jean-Pierre Jouanolou ³

Proceedings of the American Mathematical Society 137, 6 (2009) 1855-1865

Abstract: 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 a graded part of the symmetric algebra is optimal. Then we show that the extraneous factor that may appear in the process splits into a product a 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.

a – INRIA
b – CNRS
1: GALAAD (INRIA Sophia Antipolis)
INRIA – CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS)
2: Institut de Mathématiques de Jussieu (IMJ)
CNRS : UMR7586 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot
3: Institut de Recherche Mathématique Avancée (IRMA)
CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I

inria-00104191, version 2
http://hal.inria.fr/inria-00104191
oai:hal.inria.fr:inria-00104191
From: Laurent Busé <>
Submitted on: Thursday, 13 September 2007 11:29:01
Updated on: Wednesday, 3 March 2010 15:08:52

See detailed view

Associated documents

PS :

PDF :

Export

Bibtex EndNote TEI RefWorks

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="article"><head>Articles in peer-reviewed journal</head>
<biblStruct type="article" xml:id="inria-00104191"><analytic>
<author><persName><forename>Laurent</forename><surname>Busé</surname></persName>
<affiliation>
<orgName type="laboratory">INRIA Sophia Antipolis</orgName>
<orgName type="team">GALAAD</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">CNRS : UMR6621</orgName>
<orgName type="institution">Université de Nice Sophia Antipolis (UNS)</orgName>
</affiliation>
</author>
<author><persName><forename>Marc</forename><surname>Chardin</surname></persName>
<affiliation>
<orgName type="laboratory">IMJ</orgName>
<orgName type="team">Institut de Mathématiques de Jussieu</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR7586</orgName>
<orgName type="institution">Université Paris VI - Pierre et Marie Curie</orgName>
<orgName type="institution">Université Paris VII - Paris Diderot</orgName>
</affiliation>
</author>
<author><persName><forename>Jean-Pierre</forename><surname>Jouanolou</surname></persName>
<affiliation>
<orgName type="laboratory">IRMA</orgName>
<orgName type="team">Institut de Recherche Mathématique Avancée</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR7501</orgName>
<orgName type="institution">Université Louis Pasteur - Strasbourg I</orgName>
</affiliation>
</author>
<title type="main" level="a">Torsion of the symmetric algebra and implicitization</title></analytic><monogr><title level="j" type="main">Proceedings of the American Mathematical Society</title><imprint><publisher>American Mathematical Society</publisher><biblScope type="publicationDate">2009-00-00</biblScope><biblScope type="vol">137</biblScope><biblScope type="issue">6</biblScope><biblScope type="pp">1855-1865</biblScope></imprint></monogr><idno type="HALid">http://hal.inria.fr/inria-00104191</idno><idno type="HALFile">http://hal.inria.fr/inria-00104191/PDF/extrafactor.pdf</idno></biblStruct>
</listBibl>
</listBibl>