4 papers
Apolarity for border cactus decompositions
Weronika BuczyÅska, JarosÅaw BuczyÅski
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 BuczyÅska, JarosÅaw BuczyÅski, Maciej GaÅÄ zka
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…
Families of Morse functions for manifolds with boundary
Maciej Borodzik, Weronika BuczyÅska
We study 1-parameter families of Morse functions for manifolds with boundary. We list all degeneracies that may occur in generic 1-parameter families.
Cactus varieties of sufficiently ample embeddings of projective schemes have determinantal equations
Weronika BuczyÅska, JarosÅaw BuczyÅski, Åucja 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…