Border subrank via a generalised Hilbert-Mumford criterion
<|reference_start|>Border subrank via a generalised Hilbert-Mumford criterion: We show that the border subrank of a sufficiently general tensor in $(\mathbb{C}^n)^{\otimes d}$ is $\mathcal{O}(n^{1/(d-1)})$ for $n \to \infty$. Since this matches the growth rate $\Theta(n^{1/(d-1)})$ for the generic (non-border) subrank recently established by Derksen-Makam-Zuiddam, we find that the generic border subrank has the same growth rate. In our proof, we use a generalisation of the Hilbert-Mumford criterion that we believe will be of independent interest.<|reference_end|>
@article{biaggi2024border,
    title={Border subrank via a generalised Hilbert-Mumford criterion},
    author={Benjamin Biaggi, Chia-Yu Chang, Jan Draisma, Filip Rupniewski},
    journal={arXiv preprint arXiv:2402.10674},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.10674},
    primaryClass={math.AG cs.CC}
}