On the geometry of geometric rank

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.

References in corpus (1)

• Bad and good news for Strassen's laser method: Border rank of the 3x3 permanent and strict submultiplicativity