6 papers
Cactus barriers
Jarosław Buczyński
Determinantal methods for bounding the rank and border rank of tensors or polynomials are subject to a major barrier. For instance, it is known that using determinantal methods one…
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…
Cactus scheme, catalecticant minors, and scheme theoretic equations
Jarosław Buczyński, Hanieh Keneshlou
The -th cactus variety of a subvariety in a projective space generalizes the -th secant variety of and it is defined using linear spans of finite subschemes of of…
Maps of Mori Dream Spaces in Cox coordinates. Part I: existence of descriptions
Jarosław Buczyński, Oskar Kędzierski
Any rational map between affine spaces, projective spaces or toric varieties can be described in terms of their affine, homogeneous, or Cox coordinates. We show an analogous statem…