On the cactus rank of cubic forms

Authors:
Alessandra Bernardi;Kristian Ranestad
Affiliations:
GALAAD, INRIA Méditerranée, 2004 route del Lucioles, BP 93, F-06902 Sophia Antipolis Cedex, France;Matematisk institutt, Universitetet i Oslo, PO Box 1053, Blindern, NO-0316 Oslo, Norway
Venue:
Journal of Symbolic Computation
Year:
2013

Citing 2
Cited 0

On the Ranks and Border Ranks of Symmetric Tensors

Foundations of Computational Mathematics
Computing symmetric rank for symmetric tensors

Journal of Symbolic Computation

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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=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.