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arXiv · 2007.09962

On a geometric method for the identifiability of forms

Andrea Mazzon
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Abstract

We introduce a new criterion which tests if a given decomposition of a given ternary form $T$ of even degree is unique. The criterion is based on the analysis of the Hilbert function of the projective set of points $Z$ associated to the decomposition, and on the Terracini's Lemma which describes tangent spaces to secant varieties. The criterion works in a range for the length of the decomposition which is equivalent to the range in which the reshaped Kruskal's criterion (see [1]) works. Our criterion determines an algorithm for the identifiability of $T$ which is sensibly faster than algorithms based on the reshaped Kruskal's criterion, especially when the set of points $Z$ is not in general position.

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Andrea Mazzon. 2020-07-20. On a geometric method for the identifiability of forms. https://doi.org/10.1007/s40574-019-00209-5

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