Classification and degenerations of small minimal border rank tensors via modules
<|reference_start|>Classification and degenerations of small minimal border rank tensors via modules: We give a self-contained classification of $1_*$-generic minimal border rank tensors in $C^m \otimes C^m \otimes C^m$ for $m \leq 5$. Together with previous results, this gives a classification of all minimal border rank tensors in $C^m \otimes C^m \otimes C^m$ for $m \leq 5$: there are $37$ isomorphism classes. We fully describe possible degenerations among the tensors. We prove that there are no $1$-degenerate minimal border rank tensors in $C^m \otimes C^m \otimes C^m $ for $m \leq 4$.<|reference_end|>
@article{jagiełła2024classification,
    title={Classification and degenerations of small minimal border rank tensors
  via modules},
    author={Jakub Jagie{l}{l}a, Joachim Jelisiejew},
    journal={arXiv preprint arXiv:2409.06025},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.06025},
    primaryClass={math.AG cs.CC math.AC}
}