7 papers
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…
Decompositions of Chow rings of direct sums of matroids
Paweł Pielasa
We prove two dual recursive decompositions as a graded -module of the Chow ring o…
Cohomology of the Quot scheme of an infinite affine space
Paweł Pielasa
We study the Quot scheme of points . We exhibit and compute the cohomology of explicit loci in $\mathrm{Quot}_d(\mathcal{O…
On gamma-vectors and Chow polynomials of restrictions of reflection arrangements
Sebastian Degen, Lisa Henetmayr, Magdaléna Mišinová +2
Simplicial arrangements are a special class of hyperplane arrangements, having the property that every chamber is a simplicial cone. It is known that the simpliciality property is…
Characteristic numbers of algebras
Jakub Jagiełła, Paweł Pielasa, Anatoli Shatsila
We introduce characteristic numbers of a finite commutative unital -algebra, which are numerical invariants arising from algebraic intersection theory. We characterize…
On the construction of a counterexample to Strassen's rank additivity conjecture
Viktoriia Borovik, Cosimo Flavi, Paweł Pielasa +2
The rank additivity conjecture, first formulated by Volker Strassen in 1973, states that the rank of the direct sum of two independent tensors is equal to the sum of their individu…