On degenerate geometric rank
arXiv:2607.18898
Abstract
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 sufficient criterion for when such a tensor cannot be lifted to a larger tensor and characterize those tensors for which the degeneracy is caused by the rank locus. We also provide new examples of tensors with degenerate geometric rank stemming from nonlinear loci.
10 pages