On the number of Waring decompositions for a generic polynomial vector

DOI10.1016/j.jpaa.2017.05.016zbMath1390.14158arXiv1601.01869OpenAlexW2230967152MaRDI QIDQ1678283

Giorgio Ottaviani, Massimiliano Mella, Francesco Galuppi, Elena Angelini

Publication date: 14 November 2017

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.01869

zbMATH Keywords

Waring decompositions

Mathematics Subject Classification ID

Projective techniques in algebraic geometry (14N05)

Related Items

Catalecticant intersections and confinement of decompositions of forms ⋮ A note on the simultaneous Waring rank of monomials ⋮ Distinguishing secant from cactus varieties ⋮ Identifiability of an X-Rank Decomposition of Polynomial Maps ⋮ Generic identifiability of pairs of ternary forms ⋮ A counterexample to a conjecture on simultaneous Waring identifiability ⋮ Complete intersections on Veronese surfaces ⋮ Typical and admissible ranks over fields ⋮ Waring decompositions and identifiability via Bertini and Macaulay2 software ⋮ Identifiability of homogeneous polynomials and Cremona transformations ⋮ Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank ⋮ The Hitchhiker guide to: secant varieties and tensor decomposition

Uses Software

• Macaulay2
• Bertini
• NumericalAlgebraicGeometry

Cites Work

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• Eigenvectors of tensors and algorithms for Waring decomposition
• Birational aspects of the geometry of varieties of sums of powers
• Varieties with minimal secant degree and linear systems of maximal dimension on surfaces
• Decomposing tensors into frames
• The blowing up Horace method: Application to interpolation in degree four
• On Waring's problem for several algebraic forms
• Grassmann secants, identifiability, and linear systems of tensors
• On the hypersurface of Lüroth quartics
• Identifiability of homogeneous polynomials and Cremona transformations
• Homotopy techniques for tensor decomposition and perfect identifiability
• Weakly defective varieties
• Tensor decompositions for learning latent variable models
• Singularities of linear systems and the Waring problem
• Base loci of linear systems and the Waring problem
• Varieties of sums of power
• The Possible Dimensions of the Higher Secant Varieties
• Connectivity and Irreducibility of Algebraic Varieties of Finite Unit Norm Tight Frames