The border rank of the $4 \times 4$ determinant tensor is twelve
Algebraic Geometry
2025-10-14 v1 Commutative Algebra
Abstract
We show that the border rank of the determinant tensor is at least over , using the fixed ideal theorem introduced by Buczy\'nska-Buczy\'nski and the method by Conner-Harper-Landsberg. Together with the known upper bound, this implies that the border rank is exactly .
Cite
@article{arxiv.2510.11051,
title = {The border rank of the $4 \times 4$ determinant tensor is twelve},
author = {Jong In Han and Jeong-Hoon Ju and Yeongrak Kim},
journal= {arXiv preprint arXiv:2510.11051},
year = {2025}
}
Comments
16 pages, comments are welcome