Special fibers of coordinate sections of Hankel Matrices
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911325599301632 |
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| author | Ansaldi, Katie Lira, Dayane Mostafazadehfard, Maral Saloni, Kumari Seccia, Lisa |
| author_facet | Ansaldi, Katie Lira, Dayane Mostafazadehfard, Maral Saloni, Kumari Seccia, Lisa |
| contents | We investigate the special fibers associated with certain coordinate sections of Hankel determinantal ideals. We provide explicit descriptions of their defining equations, showing that these equations admit a natural matrix structure. In particular, we prove that they are Cohen-Macaulay and cannot, in general, be minimally generated only by quadrics and cubics. Instead, we show that the degrees of their minimal generators grow with the size of the minors involved. In one case, we also prove that the Rees algebra is of fiber type. Additionally, we compute algebraic invariants of these special fibers. Our results partially build on and extend the work of Ramkumar and Sammartano on $2$-determinantal ideals and answer some of the questions posed by Cunha, Mostafazadehfard, Ramos, and Simis in earlier work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16165 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Special fibers of coordinate sections of Hankel Matrices Ansaldi, Katie Lira, Dayane Mostafazadehfard, Maral Saloni, Kumari Seccia, Lisa Commutative Algebra 13A30, 14M12 (Primary) 13D02, 13H15 (Secondary) We investigate the special fibers associated with certain coordinate sections of Hankel determinantal ideals. We provide explicit descriptions of their defining equations, showing that these equations admit a natural matrix structure. In particular, we prove that they are Cohen-Macaulay and cannot, in general, be minimally generated only by quadrics and cubics. Instead, we show that the degrees of their minimal generators grow with the size of the minors involved. In one case, we also prove that the Rees algebra is of fiber type. Additionally, we compute algebraic invariants of these special fibers. Our results partially build on and extend the work of Ramkumar and Sammartano on $2$-determinantal ideals and answer some of the questions posed by Cunha, Mostafazadehfard, Ramos, and Simis in earlier work. |
| title | Special fibers of coordinate sections of Hankel Matrices |
| topic | Commutative Algebra 13A30, 14M12 (Primary) 13D02, 13H15 (Secondary) |
| url | https://arxiv.org/abs/2512.16165 |