Bernardi, Alessandra ; Ranestad, Kristian
(2011)
The cactus rank of cubic forms.
[Preprint]
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Abstract
We prove that the smallest degree of an apolar $0$-dimensional scheme to 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. When $n=8$ we show that the bound is sharp, i.e. the smallest degree of an apolar subscheme is $18$.
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