Equations of tensor eigenschemes

Beorchia, Valentina; Galuppi, Francesco; Venturello, Lorenzo

doi:10.48550/arxiv.2205.04413

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…Finally, in the case n = 3 = d, some partial results are given in [5], and for n ≥ 3, a characterization of the sets of determinantal equations is given in [4]. As far as we know, a general description of the geometry of eigenpoints in the projective space is widely open.…”

Section: Introductionmentioning

confidence: 99%

Configurations of eigenpoints

Beorchia¹,

Miró‐Roig²

2022

Preprint

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This note is motivated by the Question 16 of http://cubics.wikidot.com (see also [16]): Which configurations of 15 points in P 3 arise as eigenpoints of a cubic surface? We prove that a general eigenscheme in P n is the complete intersection of two suitable smooth determinantal curves on a smooth determinantal surface. Moreover, we prove that the converse result holds if n = 3, providing an answer in any degree to the cited question. Finally, we show that any general set of points in P 3 can be enlarged to an eigenscheme of a partially symmetric tensor.

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Section: Introductionmentioning

confidence: 99%

Configurations of eigenpoints

Beorchia¹,

Miró‐Roig²

2022

Preprint

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“…On the other hand, in some examples we provide explicitly the equations of Z T which are linearly independent from the ones of H T , and our cohomology computations allow us to guarantee that the new equations are sufficient to obtain Z T . This part of the paper is closely related to the characterization of determinantal relations among singular k-tuples that is studied in the recent paper [BGV22].…”

Section: Introductionmentioning

confidence: 99%

The span of singular tuples of a tensor beyond the boundary format

Sodomaco¹,

Turatti²

2022

Preprint

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We study the dimension of the span of singular tuples of a tensor T without assuming that the ambient tensor space is of sub-boundary format. In particular, we concentrate on special order three tensors as well as order-k tensors of format (2, . . . , 2, n). In some of the mentioned formats, we show that the tensor T belongs to the span of its singular k-tuples. Furthermore, we conjecture that the dimension of the span of singular k-tuples stabilizes beyond the boundary format when k > 3.

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Equations of tensor eigenschemes

Cited by 2 publications

References 7 publications

Configurations of eigenpoints

Configurations of eigenpoints

The span of singular tuples of a tensor beyond the boundary format

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