45 citations · 51 across the 5 of their papers we have counts for
8 papers · 1 filter
Apolarity for border cactus decompositions
Weronika Buczyńska, Jarosław Buczyński
The border apolarity technique was introduced in our earlier work for secant varieties over complex numbers. We extend the theory to cactus varieties of toric varieties over any al…
Grassmann cactus variety and socle dimension
Weronika Buczyńska, Jarosław Buczyński, Maciej Gałązka
Grassmann cactus variety is a common generalisation of Grassmann secant variety and cactus variety. In their definitions one considers the vector spaces of fixed dimension that are…
Cactus varieties of sufficiently ample embeddings of projective schemes have determinantal equations
Weronika Buczyńska, Jarosław Buczyński, Łucja Farnik
For a fixed projective scheme X, a property P of line bundles is satisfied by sufficiently ample line bundles if there exists a line bundle L_0 on X such that P(L) holds for any L…
Apolarity, border rank and multigraded Hilbert scheme
Weronika Buczyńska, Jarosław Buczyński
We introduce an elementary method to study the border rank of polynomials and tensors, analogous to the apolarity lemma. This can be used to describe the border rank of all cases u…
Hackbusch Conjecture on tensor formats
Weronika Buczyńska, Jarosław Buczyński, Mateusz Michałek
We prove a conjecture of W. Hackbusch about tensor network states related to a perfect binary tree and train track tree. Tensor network states are used to present seemingly complic…
Apolarity and direct sum decomposability of polynomials
Weronika Buczyńska, Jarosław Buczyński, Johannes Kleppe +1
A polynomial is a direct sum if it can be written as a sum of two non-zero polynomials in some distinct sets of variables, up to a linear change of variables. We analyze criteria f…
Waring decompositions of monomials
Weronika Buczyńska, Jarosław Buczyński, Zach Teitler
A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Wa…
Secant varieties to high degree Veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes
Weronika Buczyńska, Jarosław Buczyński
We study the secant varieties of the Veronese varieties and of Veronese reembeddings of a smooth projective variety. We give some conditions, under which these secant varieties are…