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 eprints
 Pub Date:
 April 2015
 arXiv:
 arXiv:1504.00547
 Bibcode:
 2015arXiv150400547C
 Keywords:

 Mathematics  Algebraic Geometry;
 14C20;
 14N05;
 14Q15;
 15A69;
 15A72
 EPrint:
 20 pages, two M2 files as ancillary files