From non Defectivity to Identifiability

We give Margin NotesMargin notes provide warnings and explanations regarding changes in the text. No need to respond to these notes unless you disagree with the change. However, please respond to queries (if any).Red parts indicate major changes! Please check them carefully.an almost asymptotically sharp bound for the non-secant defectiveness and identifiability of Segre-Veronese varieties. We also provide new examples of defective Segre-Veronese varieties, and implement our methods in Magma. Finally, we give two applications of our techniques: we classify possibly singular 2-secant defective toric surfaces and we study secant defectiveness of Losev-Manin spaces.

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“…Since entries may be mismatched, please carefully double-check each one. Are there any updates on [14,28]?…”

Section: Note 11mentioning

confidence: 99%

On secant defectiveness and identifiability of Segre–Veronese varieties

2022

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“…This is of particular interest in the cases of Segre-Veronese varieties due to its applications to tensor decompositions. In [CM19], the authors relate the study of defectivity to the study of identifiability. In particular, from their main result, we can deduce that under the assumptions of Theorem 1.3 the general point of the…”

Section: Non-defectivity Via Collisions Of Fat Pointsmentioning

confidence: 99%

Secant non-defectivity via collisions of fat points

Galuppi¹,

Oneto²

2021

Preprint

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Secant defectivity of projective varieties is classically approached via dimensions of linear systems with multiple base points in general position. The latter can be studied via degenerations. We exploit a technique that allows some of the base points to collapse together. We deduce a general result which we apply to prove a conjecture by Abo and Brambilla: for c ≥ 3 and d ≥ 3, the Segre-Veronese embedding of P m × P n in bidegree (c, d) is non-defective.

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“…(1) If X is not q-tangentially weakly defective, then it is q-identifiable, that is, the map S q (X ) → S q (X ) is birational; see [6,Proposition 14].…”

Section: A Proof Of the Generalized Bronowski's Conjecture Weak Formmentioning

confidence: 99%

A matryoshka structure of higher secant varieties and the generalized Bronowski's conjecture

Choe¹,

Kwak²

2021

Preprint

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In this paper, we propose a matryoshka structure of higher secant varieties which includes many matryoshka phenomena in the category of higher secant varieties and generalizes certain celebrated classical results in the study of syzygy to higher secant varieties. For example, we prove a generalized K p,1 theorem for higher secant varieties, the syzygetic and geometric characterizations of minimal degree higher secant varieties, defined by Ciliberto and Russo ([13]), and del Pezzo higher secant varieties, newly defined in this paper, and also give the determinantal presentation of higher secant varieties having minimal degree.These results come mainly from the structure of the tangent cones to higher secant varieties and from inductive analyses of defining equations and their syzygies in relation to inner and tangential projections. For our purposes, we prove a weak form of the generalized Bronowski's conjecture due to Ciliberto and Russo ([13]) that relates the identifiability for higher secant varieties to the geometry of tangential projections.

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From non Defectivity to Identifiability

Cited by 4 publications

References 13 publications

On secant defectiveness and identifiability of Segre–Veronese varieties

On secant defectiveness and identifiability of Segre–Veronese varieties

Secant non-defectivity via collisions of fat points

A matryoshka structure of higher secant varieties and the generalized Bronowski's conjecture

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