M. Dolezálek

collaborators

5 papers

math.AG2026

On degenerate geometric rank

MatÄj DoleÅ¾Ã¡lek, PaweÅ 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 $r$ has unexpectedly large dimension. We prove a suf…

math.AG2026

Nonlinear methods for tensors: determinantal equations for secant varieties beyond cactus

MatÄj DoleÅ¾Ã¡lek, Mateusz MichaÅek

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…

math.AG2026

Secant varieties of Segre-Veronese varieties $P^{m} \times P^{n}$ embedded by $O (1, 2)$ are non-defective for $n ≫ m^{3}$ , $m \geq 3$

MatÄj DoleÅ¾Ã¡lek, Nikhil Ken

We prove that for any $m \geq 3$ , $n ≫ m^{3}$ , all secant varieties of the Segre-Veronese variety $P^{m} \times P^{n}$ have the expected dimension. This was already proved…

math.AG2025

Equivariant Tutte Polynomial

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…

math.NT2025

Extending bounds on minimal ranks of universal quadratic lattices to larger number fields

MatÄj DoleÅ¾Ã¡lek

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…

On degenerate geometric rank

Nonlinear methods for tensors: determinantal equations for secant varieties beyond cactus

Secant varieties of Segre-Veronese varieties Pm×Pn embedded by O(1,2) are non-defective for n≫m3, m≥3

Equivariant Tutte Polynomial

Extending bounds on minimal ranks of universal quadratic lattices to larger number fields

Secant varieties of Segre-Veronese varieties $P^{m} \times P^{n}$ embedded by $O (1, 2)$ are non-defective for $n ≫ m^{3}$ , $m \geq 3$