Secants, Socles and Stability
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918026818879488 |
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| author | Bertram, Aaron Ullery, Brooke |
| author_facet | Bertram, Aaron Ullery, Brooke |
| contents | The projective space of symmetric tensors of degree d can be reinterpreted as a projective space of finite, graded Gorenstein rings with socle in degree d. Via a pair of explicit stability conditions (one for even values of d and one for odd values), the space of symmetric tensors is partitioned by Harder-Narasimhan filtration type. This is worked out explicitly for low degree examples in dimension three (the projective plane) and compared with the betti tables of the Gorenstein rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Secants, Socles and Stability Bertram, Aaron Ullery, Brooke Commutative Algebra Algebraic Geometry The projective space of symmetric tensors of degree d can be reinterpreted as a projective space of finite, graded Gorenstein rings with socle in degree d. Via a pair of explicit stability conditions (one for even values of d and one for odd values), the space of symmetric tensors is partitioned by Harder-Narasimhan filtration type. This is worked out explicitly for low degree examples in dimension three (the projective plane) and compared with the betti tables of the Gorenstein rings. |
| title | Secants, Socles and Stability |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2505.14445 |