On schemes evinced by generalized additive decompositions and their regularity

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Polynomials over commutative rings (13B25) Secant varieties, tensor rank, varieties of sums of powers (14N07)

Cites Work

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Equations for secant varieties of Veronese and other varieties
Waring decompositions of monomials
A comparison of different notions of ranks of symmetric tensors
Symmetric tensor decomposition
Computing symmetric rank for symmetric tensors
Irreducibility of the Gorenstein loci of Hilbert schemes via ray families
Apolarity and direct sum decomposability of polynomials
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The Magma algebra system. I: The user language
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Apolarity, border rank, and multigraded Hilbert scheme
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Waring, tangential and cactus decompositions
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Hilbert functions and tensor analysis
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\(K3\) surfaces of genus 8 and varieties of sums of powers of cubic fourfolds
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An Introduction to Algebraic Statistics with Tensors
ON DIFFERENCES BETWEEN THE BORDER RANK AND THE SMOOTHABLE RANK OF A POLYNOMIAL
Osculating Varieties of Veronese Varieties and Their Higher Secant Varieties
Secant varieties to high degree Veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes
Waring decompositions of special ternary forms with different Hilbert functions

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