On degenerate geometric rank

2026/07/21 by Matěj Doležálek, Paweł Pielasa, Derek Wu
#math.AG

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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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