Cactus barriers
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | |
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| _version_ | 1866908828960817152 |
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| author | Buczyński, Jarosław |
| author_facet | Buczyński, Jarosław |
| contents | Determinantal methods for bounding the rank and border rank of tensors or polynomials are subject to a major barrier. For instance, it is known that using determinantal methods one cannot prove a lower bound for the border rank of a 3-way tensor of size m in each direction that exceeds 6m-4. We explain the precise geometric reason for this number (and analogous bounds in more general tensor spaces) using cactus varieties and, more generally, scheme theoretic methods in algebraic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11309 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cactus barriers Buczyński, Jarosław Algebraic Geometry 14N07 (Primary) 03D15, 14A15, 15A69 (Secondary) Determinantal methods for bounding the rank and border rank of tensors or polynomials are subject to a major barrier. For instance, it is known that using determinantal methods one cannot prove a lower bound for the border rank of a 3-way tensor of size m in each direction that exceeds 6m-4. We explain the precise geometric reason for this number (and analogous bounds in more general tensor spaces) using cactus varieties and, more generally, scheme theoretic methods in algebraic geometry. |
| title | Cactus barriers |
| topic | Algebraic Geometry 14N07 (Primary) 03D15, 14A15, 15A69 (Secondary) |
| url | https://arxiv.org/abs/2602.11309 |