The cactus rank of cubic forms - Inria - Institut national de recherche en sciences et technologies du numérique
Preprints, Working Papers, ... Year : 2011

The cactus rank of cubic forms

Alessandra Bernardi
  • Function : Author
  • PersonId : 914887
Kristian Ranestad
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  • PersonId : 911880

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)

Identifiers

  • HAL Id : inria-00630456 , version 2

Cite

Alessandra Bernardi, Kristian Ranestad. The cactus rank of cubic forms. 2011. ⟨inria-00630456v2⟩
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