On generic identifiability of symmetric tensors of subgeneric rank

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.

20 pages, two M2 files as ancillary files; v2 contains some changes in section 5

References in corpus (2)

• An algorithm for generic and low-rank specific identifiability of complex tensors
• Identifiability of homogeneous polynomials and Cremona Transformations

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