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arXiv · 1110.2197

On the cactus rank of cubics forms

Alessandra Bernardi·Kristian Ranestad
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Abstract

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 $2n$.

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Alessandra Bernardi, Kristian Ranestad. 2011-10-10. On the cactus rank of cubics forms. https://doi.org/10.1016/j.jsc.2012.08.001

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