Apolarity, border rank, and multigraded Hilbert scheme
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Publication:2059024
DOI10.1215/00127094-2021-0048zbMath1481.14006arXiv1910.01944OpenAlexW3206567653MaRDI QIDQ2059024
Jarosław Buczyński, Weronika Buczyńska
Publication date: 13 December 2021
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1910.01944
Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Parametrization (Chow and Hilbert schemes) (14C05) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Multilinear algebra, tensor calculus (15A69)
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Cites Work
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- Waring decompositions of monomials
- Quasicoherent sheaves on toric schemes
- A comparison of different notions of ranks of symmetric tensors
- On the third secant variety
- Lower bound for ranks of invariant forms
- Vector bundles give equations of cactus varieties
- Variety of power sums and divisors in the moduli space of cubic fourfolds
- Computing symmetric rank for symmetric tensors
- Irreducibility of the Gorenstein loci of Hilbert schemes via ray families
- On the geometry of some special projective varieties
- Apolarity and direct sum decomposability of polynomials
- On the ranks and border ranks of symmetric tensors
- Hilbert schemes of 8 points
- The Magma algebra system. I: The user language
- Finite schemes and secant varieties over arbitrary characteristic
- Varieties of apolar subschemes of toric surfaces
- The Hilbert scheme of 11 points in \(\mathbb{A}^3\) is irreducible
- Power sums, Gorenstein algebras, and determinantal loci. With an appendix `The Gotzmann theorems and the Hilbert scheme' by Anthony Iarrobino and Steven L. Kleiman
- Ranks of tensors and a generalization of secant varieties
- On tensors of border rank \(l\) in \({\mathbb C}^{m\times n\times l}\)
- The solution to the Waring problem for monomials and the sum of coprime monomials
- Vanishing Hessian, wild forms and their border VSP
- On the rank of a symmetric form
- $K3$ surfaces of genus 8 and varieties of sums of powers of cubic fourfolds
- Stratification of the fourth secant variety of Veronese varieties via the symmetric rank
- Maps of toric varieties in Cox coordinates
- Varieties of sums of power
- Multigraded Hilbert schemes
- On Strassen's Rank Additivity for Small Three-way Tensors
- ON DIFFERENCES BETWEEN THE BORDER RANK AND THE SMOOTHABLE RANK OF A POLYNOMIAL
- On the Geometry of Border Rank Decompositions for Matrix Multiplication and Other Tensors with Symmetry
- Geometry and Complexity Theory
- Secant varieties to high degree Veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes
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