On the geometry of geometric rank

12/08/2020

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by   Runshi Geng, et al.

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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⊗ C^3⊗ C^3, classification of tensors with geometric rank two, and showing that upper bounds on geometric rank imply lower bounds on tensor rank.