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.

翻译：我们最近对Kopparty等人引进的 " 高压几何等级 " 进行了几何研究。 研究结果包括:以$C3\otimes C3\otimes C3\otimes C3$对低劣几何等级的 " 高压数 " 进行分类,对高压数进行二等几何等级的 " 高限 " 分类,并表明几何等级的 " 高限 " 意味着 " 高压等级 " 的 " 低限 " 。