5 papers
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…
Families of Morse functions for manifolds with boundary
Maciej Borodzik, Weronika Buczyńska
We study 1-parameter families of Morse functions for manifolds with boundary. We list all degeneracies that may occur in generic 1-parameter families.
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…