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Journal Articles Journal of Symbolic Computation Year : 2013

On the cactus rank of cubic forms

Alessandra Bernardi
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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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Dates and versions

inria-00630456 , version 1 (10-10-2011)
inria-00630456 , version 2 (24-10-2011)
inria-00630456 , version 3 (28-11-2011)

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Cite

Alessandra Bernardi, Kristian Ranestad. On the cactus rank of cubic forms. Journal of Symbolic Computation, 2013, 50, pp.291-297. ⟨10.1016/j.jsc.2012.08.001⟩. ⟨inria-00630456v3⟩
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