On the identifiability of binary Segre products

DOI10.1090/S1056-3911-2011-00592-4zbMath1273.14107arXiv1105.3643WikidataQ60307026 ScholiaQ60307026MaRDI QIDQ4904368

Cristiano Bocci, Luca Chiantini

Publication date: 29 January 2013

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.3643

zbMATH Keywords

tensor decompositionsecant VarietiesSegre Varieties

Mathematics Subject Classification ID

Divisors, linear systems, invertible sheaves (14C20) Projective techniques in algebraic geometry (14N05)

Related Items

Identifiability for the k-secant variety of the Segre-Veronese varieties ⋮ Effective Criteria for Specific Identifiability of Tensors and Forms ⋮ Grassmann secants, identifiability, and linear systems of tensors ⋮ Embedded varieties, \(X\)-ranks and uniqueness or finiteness of the solutions ⋮ From non-defectivity to identifiability ⋮ An algorithm for the non-identifiability of rank-3 tensors ⋮ Hadamard products of linear spaces ⋮ On generic identifiability of symmetric tensors of subgeneric rank ⋮ A uniqueness result on the decompositions of a bi-homogeneous polynomial ⋮ Refined methods for the identifiability of tensors ⋮ Typical and admissible ranks over fields ⋮ Real identifiability vs. complex identifiability ⋮ Unnamed Item ⋮ Equations for the Fifth Secant Variety of Segre Products of Projective Spaces ⋮ Partially symmetric tensor rank: the description of the non-uniqueness case for low rank ⋮ Identifiability of rank-3 tensors ⋮ Mixture decompositions of exponential families using a decomposition of their sample spaces ⋮ The Hitchhiker guide to: secant varieties and tensor decomposition

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• Unnamed Item
• The effect of points fattening on postulation
• Identifiability of parameters in latent structure models with many observed variables
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
• An application of classical invariant theory to identifiability in nonparametric mixtures.
• Ranks of tensors, secant varieties of Segre varieties and fat points
• Weakly defective varieties
• Secant varieties of ℙ¹×⋯×ℙ¹ (𝕟-times) are NOT defective for 𝕟≥5
• Induction for secant varieties of Segre varieties
• Terracini's Lemma and the Secant Variety of a Curve
• Joins and higher secant varieties.
• Varieties with one apparent double point
• ON THE CONCEPT OF k-SECANT ORDER OF A VARIETY