6 papers
Geometric and homological interpretations of tensor flattenings
Matěj Doležálek, Jakub Jagiełła, Piotr Oszer +2
We relate several nonlinear flattenings of structure tensors of finite algebras and modules to their algebraic and homological invariants. Since smoothability of algebras is equiva…
On degenerate geometric rank
Matěj Doležálek, Paweł Pielasa, Derek Wu
A tensor of degenerate geometric rank corresponds to a linear space of matrices in which some locus of matrices of rank at most has unexpectedly large dimension. We prove a suf…
Nonlinear methods for tensors: determinantal equations for secant varieties beyond cactus
Matěj Doležálek, Mateusz Michałek
We present a family of flattening methods of tensors which we call Kronecker-Koszul flattenings, generalizing the famous Koszul flattenings and further equations of secant varietie…
Extending bounds on minimal ranks of universal quadratic lattices to larger number fields
Matěj Doležálek
There exist numerous results in the literature proving that within certain families of totally real number fields, the minimal rank of a universal quadratic lattice over such a fie…
Secant varieties of Segre-Veronese varieties embedded by are non-defective for ,
Matěj Doležálek, Nikhil Ken
We prove that for any , , all secant varieties of the Segre-Veronese variety have the expected dimension. This was already proved…
Equivariant Tutte Polynomial
Mario Bauer, Matěj Doležálek, Magdaléna Mišinová +2
We use the equivariant cohomology ring of the permutohedral variety to study matroids and their invariants. Investigating the pushforward of matroid Chern classes defined by A. Ber…