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math.AG2026
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…
math.AG2026
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…
math.AG2026
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…