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On the cactus rank of cubic forms

Alessandra Bernardi 1 Kristian Ranestad 2 
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
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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https://hal.inria.fr/inria-00630456
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Submitted on : Monday, November 28, 2011 - 6:30:25 PM
Last modification on : Thursday, August 4, 2022 - 4:52:37 PM
Long-term archiving on: : Sunday, December 4, 2016 - 8:28:55 PM

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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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