Resultants of determinantal varieties

Laurent Busé 1
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct generalization of the resultant of a very ample vector bundle introduced by Gelfand, Kapranov et Zelevinsky, it corresponds to a necessary and sufficient condition so that a given morphism between two vector bundles on a projective variety X has rank lower or equal to a given integer in at least one point. First some conditions are given for the existence of such a resultant and it is showed how to compute explicitly its degree. Then a result of A. Lascoux is used to obtain it as a determinant of a certain complex. Finally some more detailed results in the particular case where X is a projective space are exposed.
Type de document :
Article dans une revue
Journal of Pure and Applied Algebra, Elsevier, 2004, 193 (1-3), pp.71--97
Liste complète des métadonnées

Littérature citée [14 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00098680
Contributeur : Laurent Busé <>
Soumis le : lundi 25 septembre 2006 - 22:14:08
Dernière modification le : vendredi 12 janvier 2018 - 01:49:33
Document(s) archivé(s) le : jeudi 20 septembre 2012 - 10:56:01

Fichier

Identifiants

  • HAL Id : inria-00098680, version 1

Collections

Citation

Laurent Busé. Resultants of determinantal varieties. Journal of Pure and Applied Algebra, Elsevier, 2004, 193 (1-3), pp.71--97. 〈inria-00098680〉

Partager

Métriques

Consultations de la notice

268

Téléchargements de fichiers

139