2019
DOI: 10.1007/s40574-019-00209-5
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On a geometric method for the identifiability of forms

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… Show more

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Cited by 3 publications
(5 citation statements)
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“…It is a standard consequence of the Terracini's construction that if T has infinitely many decompositions, then condition c) cannot hold (see e.g. Lemma 6.5 of [12] or Proposition 6 of [25]).…”
Section: Preliminariesmentioning
confidence: 99%
“…It is a standard consequence of the Terracini's construction that if T has infinitely many decompositions, then condition c) cannot hold (see e.g. Lemma 6.5 of [12] or Proposition 6 of [25]).…”
Section: Preliminariesmentioning
confidence: 99%
“…By the AHThm, a general set S of cardinality 12 in P 2 is not the set of nodes of septic curves. Let us show the existence of loci of codimension 1 in (P 2 ) (12) formed by sets of nodes of irreducible septic curves.…”
Section: Veronese Varieties and High Rankmentioning
confidence: 99%
“…By [15], a general septic of genus 3 cannot share the set of nodes with another septic. Thus we have a 23-dimensional component of the Terracini locus in (P 2 ) (12) .…”
Section: Veronese Varieties and High Rankmentioning
confidence: 99%
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