Towards a geometric approach to Strassen’s asymptotic rank conjecture
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- Towards a geometric approach to Strassen’s asymptotic rank conjecture
Accepted author manuscript, 286 KB, PDF document
We make a first geometric study of three varieties in Cm⊗ Cm⊗ Cm (for each m), including the Zariski closure of the set of tight tensors, the tensors with continuous regular symmetry. Our motivation is to develop a geometric framework for Strassen’s 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. We prove that this dimension equals the dimension of the set of oblique tensors, a less restrictive class introduced by Strassen.
Original language | English |
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Journal | Collectanea Mathematica |
Volume | 72 |
Issue number | 1 |
Pages (from-to) | 63-86 |
ISSN | 0010-0757 |
DOIs | |
Publication status | Published - 2021 |
- Asymptotic rank, Matrix multiplication complexity, Slice rank, Tensor rank
Research areas
ID: 243015707