Waring-like decompositions of polynomials. I.

DOI10.1016/j.laa.2017.07.021zbMath1372.14047arXiv1511.07789OpenAlexW2268704426MaRDI QIDQ2404976

Luca Chiantini, Alessandro Oneto, Maria Virginia Catalisano, Anthony V. Geramita

Publication date: 21 September 2017

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.07789

zbMATH Keywords

polynomialssecant varietiesWaring problems

Mathematics Subject Classification ID

Computational aspects of higher-dimensional varieties (14Q15) Special varieties (14M99) Polynomials, factorization in commutative rings (13P05) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Projective techniques in algebraic geometry (14N05)

Related Items

Most secant varieties of tangential varieties to Veronese varieties are nondefective ⋮ Waring, tangential and cactus decompositions ⋮ Skew-symmetric tensor decomposition ⋮ Unnamed Item ⋮ Algebraic stories from one and from the other pockets ⋮ All secant varieties of the Chow variety are nondefective for cubics and quaternary forms ⋮ Almost all subgeneric third-order Chow decompositions are identifiable ⋮ The Hitchhiker guide to: secant varieties and tensor decomposition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the variety parameterizing completely decomposable polynomials
• On the ranks and border ranks of symmetric tensors
• Secant varieties to osculating varieties of Veronese embeddings of \(\mathbb P^n\)
• The Veronese variety and catalecticant matrices
• Fat points, inverse systems, and piecewise polynomial functions
• Decomposition of quantics in sums of powers of linear forms
• On equations defining coincident root loci.
• On Waring's problem for several algebraic forms
• Invariant equations defining coincident root loci
• Power sums, Gorenstein algebras, and determinantal loci. With an appendix `The Gotzmann theorems and the Hilbert scheme' by Anthony Iarrobino and Steven L. Kleiman
• The solution to the Waring problem for monomials and the sum of coprime monomials
• Varieties of completely decomposable forms and their secants
• Expressing a general form as a sum of determinants
• Secant varieties of the varieties of reducible hypersurfaces in \(\mathbb{P}^n\)
• On the secant varieties to the tangent developable of a Veronese variety
• On the secant varieties to the tangential varieties of a Veronesean
• Generic forms of low Chow rank
• SECANTS TO THE VARIETY OF COMPLETELY REDUCIBLE FORMS AND THE HILBERT FUNCTION OF THE UNION OF STAR-CONFIGURATIONS
• The Waring Locus of Binary Forms
• Most secant varieties of tangential varieties to Veronese varieties are nondefective
• Decomposable Ternary Cubics
• Inner Approximations for Polynomial Matrix Inequalities and Robust Stability Regions