On generic identifiability of symmetric tensors of subgeneric rank

  title={On generic identifiability of symmetric tensors of subgeneric rank},
  author={L. Chiantini and G. Ottaviani and Nick Vannieuwenhoven},
  journal={Transactions of the American Mathematical Society},
  • L. Chiantini, G. Ottaviani, Nick Vannieuwenhoven
  • Published 2015
  • Mathematics
  • Transactions of the American Mathematical Society
  • We prove that the general symmetric tensor in SdCn+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 � 4 we rely on known results on weak defectivity by Ballico, Ciliberto, Chiantini, and Mella. 

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