A geometric study of Strassen's asymptotic rank conjecture and its variants
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We establish basic information about the set of tight tensors, the tensors with continuous regular symmetry. Our motivation is Strassen's astounding asymptotic rank conjecture that the asymptotic rank of any tight tensor is minimal. In particular, we determine the dimension of the set of tight tensors. Surprisingly we prove this dimension equals the dimension of the set of oblique tensors, a less restrictive class of tensors that Strassen identified as useful for his laser method.
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