On generic identifiability of symmetric tensors of subgeneric rank

Chiantini, Luca; Ottaviani, Giorgio; Vannieuwenhoven, Nick

doi:10.1090/tran/6762

On generic identifiability of symmetric tensors of subgeneric rank
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by Luca Chiantini, Giorgio Ottaviani and Nick Vannieuwenhoven PDF

Trans. Amer. Math. Soc. 369 (2017), 4021-4042 Request permission

Abstract:

We prove that the general symmetric tensor in $S^d\mathbb {C}^{n+1}$ of rank $r$ is identifiable, provided that $r$ is smaller than the generic rank. That is, its Waring decomposition as a sum of $r$ powers of linear forms is unique. Only three exceptional cases arise, all of which were known in the literature. Our original contribution regards the case of cubics ($d=3$), while for $d\ge 4$ we rely on known results on weak defectivity by Ballico, Ciliberto, Chiantini, and Mella.

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