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arXiv · 2607.18898

On degenerate geometric rank

Matěj Doležálek·Paweł Pielasa·Derek Wu
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Abstract

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 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 $r=1$ locus. We also provide new examples of tensors with degenerate geometric rank stemming from nonlinear loci.

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Matěj Doležálek, Paweł Pielasa, Derek Wu. 2026-07-21. On degenerate geometric rank. https://arxiv.org/abs/2607.18898

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