On a geometric method for the identifiability of forms

Mazzon, Andrea

doi:10.1007/s40574-019-00209-5

Cited by 3 publications

(5 citation statements)

References 23 publications

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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%

On the description of identifiable quartics

Angelini¹,

Chiantini²

2021

Preprint

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In this paper we study the identifiability of specific forms (symmetric tensors), with the target of extending recent methods for the case of 3 variables to more general cases. In particular, we focus on forms of degree 4 in 5 variables. By means of tools coming from classical algebraic geometry, such as Hilbert function, liaison procedure and Serre's construction, we give a complete geometric description and criteria of identifiability for ranks ≥ 9, filling the gap between rank ≤ 8, covered by Kruskal's criterion, and 15, the rank of a general quartic in 5 variables. For the case r = 12, we construct an effective algorithm that guarantees that a given decomposition is unique.

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Section: Preliminariesmentioning

confidence: 99%

On the description of identifiable quartics

Angelini¹,

Chiantini²

2021

Preprint

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“…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%

“…[5]). When X is a Segre or a Veronese variety, the test on the algebraic identifiability of a tensor u ∈ S r (X) can be performed by using the following, well known fact (see [4], [3] or [12]). Proposition 6.2.…”

Section: Terracini Locus and Identifiabilitymentioning

confidence: 99%

“…, p r } does not belong to the Terracini locus. A way to do that, in the case of tensors, is illustrated in the algorithms of [3] and [12].…”

Section: Terracini Locus and Identifiabilitymentioning

confidence: 99%

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On the Terracini locus of projective varieties

Ballico¹,

Chiantini²

2020

Preprint

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We introduce and study properties of the Terracini locus of projective varieties X, which is the locus of finite sets S ⊂ X such that 2S fails to impose independent conditions to a linear system L. Terracini loci are relevant in the study of interpolation problems over double points in special position, but they also enter naturally in the study of special loci contained in secant varieties to projective varieties. We find some criteria which exclude that a set S belongs to the Terracini locus. Furthermore, in the case where X is a Veronese variety, we bound the dimension of the Terracini locus and we determine examples in which the locus has codimension 1 in the symmetric product of X.

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On the Terracini Locus of Projective Varieties

Ballico

Chiantini

2021

Milan J. Math.

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We introduce and study properties of the Terracini locus of projective varieties X, which is the locus of finite sets $$S \subset X$$ S ⊂ X such that 2S fails to impose independent conditions to a linear system L. Terracini loci are relevant in the study of interpolation problems over double points in special position, but they also enter naturally in the study of special loci contained in secant varieties to projective varieties.We find some criteria which exclude that a set S belongs to the Terracini locus. Furthermore, in the case where X is a Veronese variety, we bound the dimension of the Terracini locus and we determine examples in which the locus has codimension 1 in the symmetric product of X.

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On a geometric method for the identifiability of forms

Cited by 3 publications

References 23 publications

On the description of identifiable quartics

On the description of identifiable quartics

On the Terracini locus of projective varieties

On the Terracini Locus of Projective Varieties

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