The border rank of the $4 \times 4$ determinant tensor is twelve
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915549421764608 |
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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 |