On the discriminant scheme of homogeneous polynomials - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Mathematics in Computer Science Année : 2014

On the discriminant scheme of homogeneous polynomials

Résumé

In this paper, the discriminant scheme of homogeneous polynomials is studied in two particular cases: the case of a single homogeneous polynomial and the case of a collection of n-1 homogeneous polynomials in n variables. In both situations, a normalized discriminant polynomial is defined over an arbitrary commutative ring of coefficients by means of the resultant theory. An extensive formalism for this discriminant is then developed, including many new properties and computational rules. Finally, it is shown that this discriminant polynomial is faithful to the geometry: it is a defining equation of the discriminant scheme over a general coefficient ring k, typically a domain, if 2 is not equal to 0 in k. The case where 2 is equal to 0 in k is also analyzed in detail.
Fichier principal
Vignette du fichier
disc-mcs.pdf (561.97 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00747930 , version 1 (02-11-2012)
hal-00747930 , version 2 (08-07-2014)

Identifiants

Citer

Laurent Busé, Jean-Pierre Jouanolou. On the discriminant scheme of homogeneous polynomials. Mathematics in Computer Science, 2014, Special Issue in Computational Algebraic Geometry, 8 (2), pp.175-234. ⟨10.1007/s11786-014-0188-7⟩. ⟨hal-00747930v2⟩
658 Consultations
709 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More