On defective spans of singular vector tuples beyond the boundary format
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913152130613248 |
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| author | Turatti, Ettore Teixeira Ventura, Emanuele |
| author_facet | Turatti, Ettore Teixeira Ventura, Emanuele |
| contents | In this paper, we study tensor spaces beyond the boundary format and analyze whether the general critical space coincides with the general span of singular vector tuples. For all tensor spaces exceeding the boundary format by one in an arbitrary number of factors, we relate the codimension of this span within the critical space to the dimension of the kernel of a map in cohomology. Furthermore, we exhibit an infinite family of order-three tensors with a defective behavior: the general span of singular vector tuples achieves the maximum possible codimension rather than the expected minimum. Finally, we conjecture a classification of the behavior of critical spaces in this regime and draw a connection to Koszul cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22118 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On defective spans of singular vector tuples beyond the boundary format Turatti, Ettore Teixeira Ventura, Emanuele Algebraic Geometry 14N07, 15A18, 15A69 In this paper, we study tensor spaces beyond the boundary format and analyze whether the general critical space coincides with the general span of singular vector tuples. For all tensor spaces exceeding the boundary format by one in an arbitrary number of factors, we relate the codimension of this span within the critical space to the dimension of the kernel of a map in cohomology. Furthermore, we exhibit an infinite family of order-three tensors with a defective behavior: the general span of singular vector tuples achieves the maximum possible codimension rather than the expected minimum. Finally, we conjecture a classification of the behavior of critical spaces in this regime and draw a connection to Koszul cohomology. |
| title | On defective spans of singular vector tuples beyond the boundary format |
| topic | Algebraic Geometry 14N07, 15A18, 15A69 |
| url | https://arxiv.org/abs/2605.22118 |