The cactus rank of cubic forms

Details The cactus rank of cubic forms The cactus rank of cubic forms

2011-10-10

arxiv.org/abs/1110.2197v2

Mathematics

Algebraic Geometry

The last proposition in first version removed due to incomplete proof. Revision considerably shortened

Scientific paper

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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