Abstract
We use methods of algebraic geometry to find new, effective methods for detecting the identifiability of symmetric tensors. In particular, for ternary symmetric tensors T of degree 7, we use the analysis of the Hilbert function of a finite projective set, and the Cayley–Bacharach property, to prove that, when the Kruskal’s ranks of a decomposition of T are maximal (a condition which holds outside a Zariski closed set of measure 0), then the tensor T is identifiable, i.e., the decomposition is unique, even if the rank lies beyond the range of application of both the Kruskal’s and the reshaped Kruskal’s criteria.
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Acknowledgements
The first two authors are members of the Italian GNSAGA-INDAM and are supported by the Italian PRIN 2015—Geometry of Algebraic Varieties (B16J15002000005).
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Angelini, E., Chiantini, L. & Mazzon, A. Identifiability for a Class of Symmetric Tensors. Mediterr. J. Math. 16, 97 (2019). https://doi.org/10.1007/s00009-019-1363-5
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DOI: https://doi.org/10.1007/s00009-019-1363-5