The border rank of the $4 \times 4$ determinant tensor is twelve

Fuente: arXiv
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Autores principales: Han, Jong In, Ju, Jeong-Hoon, Kim, Yeongrak
Formato: Preprint
Publicado: 2025
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author Han, Jong In
Ju, Jeong-Hoon
Kim, Yeongrak
author_facet Han, Jong In
Ju, Jeong-Hoon
Kim, Yeongrak
contents We show that the border rank of the $4 \times 4$ determinant tensor is at least $12$ over $\mathbb{C}$, using the fixed ideal theorem introduced by Buczyńska-Buczyński and the method by Conner-Harper-Landsberg. Together with the known upper bound, this implies that the border rank is exactly $12$.
format Preprint
id arxiv_https___arxiv_org_abs_2510_11051
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The border rank of the $4 \times 4$ determinant tensor is twelve
Han, Jong In
Ju, Jeong-Hoon
Kim, Yeongrak
Algebraic Geometry
Commutative Algebra
14N07, 15A15
We show that the border rank of the $4 \times 4$ determinant tensor is at least $12$ over $\mathbb{C}$, using the fixed ideal theorem introduced by Buczyńska-Buczyński and the method by Conner-Harper-Landsberg. Together with the known upper bound, this implies that the border rank is exactly $12$.
title The border rank of the $4 \times 4$ determinant tensor is twelve
topic Algebraic Geometry
Commutative Algebra
14N07, 15A15
url https://arxiv.org/abs/2510.11051