Inverting catalecticants of ternary quartics

DOI10.4418/2021.76.2.14zbMath1481.14091arXiv2105.10555MaRDI QIDQ5030931

Laura Brustenga i Moncusí, Elisa Cazzador, Roser Homs

Publication date: 18 February 2022

Full work available at URL: https://arxiv.org/abs/2105.10555

zbMATH Keywords

algebraic geometrycomplete quadricscatalecticant matricesreciprocal varietyML-degree

Mathematics Subject Classification ID

Computational aspects of higher-dimensional varieties (14Q15) Secant varieties, tensor rank, varieties of sums of powers (14N07)

Uses Software

• Macaulay2
• Magma
• HomotopyContinuation
• GitHub
• LinearCovarianceModels.jl

Cites Work

• Unnamed Item
• Equations for secant varieties of Veronese and other varieties
• Lectures on algebraic statistics
• The Magma algebra system. I: The user language
• HomotopyContinuation.jl: a package for homotopy continuation in Julia
• Power sums, Gorenstein algebras, and determinantal loci. With an appendix `The Gotzmann theorems and the Hilbert scheme' by Anthony Iarrobino and Steven L. Kleiman
• On the Alexander-Hirschowitz theorem
• Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
• Estimating linear covariance models with numerical nonlinear algebra
• Exponential varieties
• Secant varieties to high degree Veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes

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