The Cactus Rank of Cubic Forms
نویسندگان
چکیده
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 ≥ 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.
منابع مشابه
[inria-00630456, v3] The cactus rank of cubic forms
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 ≥ 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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