A proof of the set-theoretic version of the salmon conjecture

Shmuel Friedland; Elizabeth Gross

A proof of the set-theoretic version of the salmon conjecture

Algebraic Geometry 2011-05-02 v2

Authors: Shmuel Friedland , Elizabeth Gross

Abstract

We show that the irreducible variety of 4 x 4 x 4 complex valued tensors of border rank at most 4 is the zero set of polynomial equations of degree 5 (the Strassen commutative conditions), of degree 6 (the Landsberg-Manivel polynomials), and of degree 9 (the symmetrization conditions).

Keywords

salmon conjecture border rank tensors polynomial equations Strassen commutative conditions Landsberg-Manivel polynomials symmetrization conditions

Cite

@article{arxiv.1104.1776,
  title  = {A proof of the set-theoretic version of the salmon conjecture},
  author = {Shmuel Friedland and Elizabeth Gross},
  journal= {arXiv preprint arXiv:1104.1776},
  year   = {2011}
}

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7 pages

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