#### Vol. 16, No. 5, 2022

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On the geometry of geometric rank

### Runshi Geng and Joseph M. Landsberg

Vol. 16 (2022), No. 5, 1141–1160
##### Abstract

We make a geometric study of the geometric rank of tensors recently introduced by Kopparty et al. Results include classification of tensors with degenerate geometric rank in ${ℂ}^{3}\otimes {ℂ}^{3}\otimes {ℂ}^{3}$, classification of tensors with geometric rank two, and showing that upper bounds on geometric rank imply lower bounds on tensor rank.

##### Keywords
geometric rank, matrix multiplication complexity, tensor rank, asymptotic rank, laser method
##### Mathematical Subject Classification
Primary: 14L30, 15A69, 68Q17