On the variety parameterizing completely decomposable polynomials - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Journal of Pure and Applied Algebra Année : 2011

On the variety parameterizing completely decomposable polynomials

Résumé

The purpose of this paper is to relate the variety parameterizing completely decomposable homogeneous polynomials of degree $d$ in $n+1$ variables on an algebraically closed field, called $\Split_{d}(\PP n)$, with the Grassmannian of $n-1$ dimensional projective subspaces of $\PP {n+d-1}$. We compute the dimension of some secant varieties to $\Split_{d}(\PP n)$ and find a counterexample to a conjecture that wanted its dimension related to the one of the secant variety to $\GG (n-1, n+d-1)$. Moreover by using an invariant embedding of the Veronse variety into the Plücker space, we are able to compute the intersection of $\GG (n-1, n+d-1)$ with $\Split_{d}(\PP n)$, some of its secant variety, the tangential variety and the second osculating space to the Veronese variety.
Fichier principal
Vignette du fichier
Arrondo_Bernardi.pdf (281.36 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00645963 , version 1 (28-11-2011)

Identifiants

Citer

Enrique Arrondo, Alessandra Bernardi. On the variety parameterizing completely decomposable polynomials. Journal of Pure and Applied Algebra, 2011, 215 (3), pp.201-220. ⟨10.1016/j.jpaa.2010.04.008⟩. ⟨hal-00645963⟩
171 Consultations
152 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More