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Abstract
A real tensor T of rank r is identifiable if it has a unique decomposition with rank 1 tensors. Sometimes identifiability fails over , for general tensors of fixed rank. This behaviour is peculiar when r is sub-generic. In several cases, the failure is due to an elliptic normal curve passing through general points of the corresponding variety
of rank 1 tensors (Segre, Veronese, Grassmann). When this happens, we prove the existence of nonempty euclidean open subsets of some varieties of rank r tensors, whose elements have several complex decompositions, but only one of them is real.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
The authors are members of the Italian GNSAGA-INDAM and are supported by the Italian PRIN 2015 - Geometry of Algebraic Varieties (B16J15002000005).