Collineation varieties of tensors
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915114738778112 |
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| author | Gesmundo, Fulvio Keneshlou, Hanieh |
| author_facet | Gesmundo, Fulvio Keneshlou, Hanieh |
| contents | In this article, we introduce the $k$-th collineation variety of a third order tensor. This is the closure of the image of the rational map of size $k$ minors of a matrix of linear forms associated to the tensor. We classify such varieties in the case of pencils of matrices, and nets of matrices of small size. We discuss the natural stratification of tensor spaces induced by the invariants and the geometric type of the collineation varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07982 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Collineation varieties of tensors Gesmundo, Fulvio Keneshlou, Hanieh Algebraic Geometry 14E05, 14M17, 14N07 In this article, we introduce the $k$-th collineation variety of a third order tensor. This is the closure of the image of the rational map of size $k$ minors of a matrix of linear forms associated to the tensor. We classify such varieties in the case of pencils of matrices, and nets of matrices of small size. We discuss the natural stratification of tensor spaces induced by the invariants and the geometric type of the collineation varieties. |
| title | Collineation varieties of tensors |
| topic | Algebraic Geometry 14E05, 14M17, 14N07 |
| url | https://arxiv.org/abs/2312.07982 |