On a geometric method for the identifiability of forms. (English) Zbl 1440.14240
The author introduce a new criterion to test if uniqueness holds for the additive decomposition of degree \(d\) forms in \(m\) variables (here mainly \(d=3\)) as a sum of \(d\)-powers of linear forms with the minimal number of addenda (up to a permutation of the addenda). It need a solution, i.e. a decomposition with say \(a\) terms. The decomposition corresponds to the union \(A\) of \(a\) points of an \((m-1)\)-dimensional projectvive space.The criterion is essentially to test the Terracini’s tangent space at these points. It is effective and it is possible to use it in some cases not covered by the reshaped Kruskal’s criterion. As a sample he proved that for any \(n\in \mathbb {N}\) if \(m=3\), \(d=2n+8\), \(a\le 3n+11\) and the Terracini’s space at \(A\) has the expscted dimension \(3a-1\), then uniqueness holds. A related quoted paper is now appeared: [E. Angelini et al., Mediter. J. Math. 16, No. 4, Paper No. 97, 14p. (2019; Zbl 1420.14099)].
Reviewer: Edoardo Ballico (Povo)
MSC:
| 14N07 | Secant varieties, tensor rank, varieties of sums of powers |
| 15A69 | Multilinear algebra, tensor calculus |
Citations:
Zbl 1420.14099References:
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