The cactus rank of cubic forms
Résumé
We prove that the smallest degree of an apolar $0$-dimensional scheme of a general cubic form in $n+1$ variables is at most $2n+2$, when $n\geq 8$, and therefore smaller than the rank of the form. For the general reducible cubic form the smallest degree of an apolar subscheme is $n+2$, while the rank is at least $2n$.
Domaines
Géométrie algébrique [math.AG]Origine | Fichiers produits par l'(les) auteur(s) |
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