90 citations · 161 across the 10 of their papers we have counts for
18 papers
Toric Sarkisov links of toric Fano varieties
Gavin Brown, Jarosław Buczyński, Alexander Kasprzyk
We explain a web of Sarkisov links that overlies the classification of Fano weighted projective spaces in dimensions 3 and 4, extending results of Prokhorov.
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…
Singular Curves of Low Degree and Multifiltrations from Osculating Spaces
Jarosław Buczyński, Nathan Ilten, Emanuele Ventura
In order to study projections of smooth curves, we introduce multifiltrations obtained by combining flags of osculating spaces. We classify all configurations of singularities occu…
On Strassen's rank additivity for small three-way tensors
Jarosław Buczyński, Elisa Postinghel, Filip Rupniewski
We address the problem of the additivity of the tensor rank. That is for two independent tensors we study if the rank of their direct sum is equal to the sum of their individual ra…
Immaculate line bundles on toric varieties
Klaus Altmann, Jarosław Buczyński, Lars Kastner +1
We call a sheaf on an algebraic variety immaculate if it lacks any cohomology including the zero-th one, that is, if the derived version of the global section functor vanishes. Suc…
Complex contact manifolds, varieties of minimal rational tangents, and exterior differential systems
Jarosław Buczyński, Giovanni Moreno
Complex contact manifolds arise naturally in differential geometry, algebraic geometry and exterior differential systems. Their classification would answer an important question ab…
Algebraic torus actions on contact manifolds
Jarosław Buczyński, Jarosław A. Wiśniewski, Andrzej Weber
We prove the LeBrun-Salamon Conjecture in low dimensions. More precisely, we show that a contact Fano manifold X of dimension 2n+1 that has reductive automorphism group of rank at…
Finite schemes and secant varieties over arbitrary characteristic
Jarosław Buczyński, Joachim Jelisiejew
We present scheme theoretic methods that apply to the study of secant varieties. This mainly concerns finite schemes and their smoothability. The theory generalises to the base fie…
Constructions of k-regular maps using finite local schemes
Jarosław Buczyński, Tadeusz Januszkiewicz, Joachim Jelisiejew +1
A continuous map from R^m to R^N or from C^m to C^N is called k-regular if the images of any points are linearly independent. Given integers m and k a problem going back to Che…
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…
Special lines on contact manifolds
Jarosław Buczyński, Grzegorz Kapustka, Michał Kapustka
In a series of two articles Kebekus studied deformation theory of minimal rational curves on contact Fano manifolds. Such curves are called contact lines. Kebekus proved that a con…
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…
On differences between the border rank and the smoothable rank of a polynomial
Weronika Buczyńska, Jarosław Buczyński
We consider higher secant varieties to Veronese varieties. Most points on the r-th secant variety are represented by a finite scheme of length r contained in the Veronese variety -…
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…
Maps of toric varieties in Cox coordinates
Gavin Brown, Jarosław Buczyński
The Cox ring provides a coordinate system on a toric variety analogous to the homogeneous coordinate ring of projective space. Rational maps between projective spaces are described…
Ranks of tensors and a generalization of secant varieties
Jarosław Buczyński, J. M. Landsberg
We introduce subspace rank as a tool for studying ranks of tensors and X-rank more generally. We derive a new upper bound for the rank of a tensor and determine the ranks of partia…
Algebraic Legendrian Varieties
Jarosław Buczyński
Real Legendrian subvarieties are classical objects of differential geometry and classical mechanics and they have been studied since antiquity. However, complex Legendrian subvarie…