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arXiv · 1504.00547

On generic identifiability of symmetric tensors of subgeneric rank

Luca Chiantini·Giorgio Ottaviani·Nick Vannieuwenhoven
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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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Luca Chiantini, Giorgio Ottaviani, Nick Vannieuwenhoven. 2015-04-02. On generic identifiability of symmetric tensors of subgeneric rank. https://doi.org/10.1090/tran/6762

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