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.

中文翻译：

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论几何秩的几何

我们对Kopparty 等人最近引入的张量的几何等级进行了几何研究。结果包括对具有退化几何等级的张量进行分类${ℂ}^3\otimes {ℂ}^3\otimes {ℂ}^3$，几何秩为二的张量分类，并表明几何秩的上限意味着张量秩的下限。