Varieties of completely decomposable forms and their secants

DOI10.1016/j.jalgebra.2013.12.027zbMath1309.14039OpenAlexW2032077863MaRDI QIDQ2253008

Hirotachi Abo

Publication date: 25 July 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2013.12.027

zbMATH Keywords

secant varietiespolynomial decomposition

Mathematics Subject Classification ID

Special varieties (14M99) Configurations and arrangements of linear subspaces (14N20)

Related Items (10)

The secant line variety to the varieties of reducible plane curves ⋮ Waring-like decompositions of polynomials. I. ⋮ Secant varieties of the varieties of reducible hypersurfaces in \(\mathbb{P}^n\) ⋮ Most secant varieties of tangential varieties to Veronese varieties are nondefective ⋮ Generic forms of low Chow rank ⋮ An explicit matrix factorization of cubic hypersurfaces of small dimension ⋮ 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

Uses Software

• Macaulay2

Cites Work

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• On the variety parameterizing completely decomposable polynomials
• The blowing up Horace method: Application to interpolation in degree four
• On apolarity and generic canonical forms
• On the Alexander-Hirschowitz theorem
• SECANTS TO THE VARIETY OF COMPLETELY REDUCIBLE FORMS AND THE HILBERT FUNCTION OF THE UNION OF STAR-CONFIGURATIONS
• Four Lectures on Secant Varieties

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