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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2015
- DOI:
- 10.48550/arXiv.1504.00547
- arXiv:
- arXiv:1504.00547
- Bibcode:
- 2015arXiv150400547C
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14C20;
- 14N05;
- 14Q15;
- 15A69;
- 15A72
- E-Print:
- 20 pages, two M2 files as ancillary files