Invariants of toric double determinantal rings
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911027450347520 |
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| author | Biermann, Jennifer De Negri, Emanuela Gasanova, Oleksandra Musapaşaoğlu, Aslı Roy, Sudeshna |
| author_facet | Biermann, Jennifer De Negri, Emanuela Gasanova, Oleksandra Musapaşaoğlu, Aslı Roy, Sudeshna |
| contents | We study a class of double determinantal ideals denoted $I_{mn}^r$, which are generated by minors of size 2, and show that they are equal to the Hibi rings of certain finite distributive lattices. We compute the number of minimal generators of $I_{mn}^r$, as well as the multiplicity, regularity, a-invariant, Hilbert function, and $h$-polynomial of the ring $R/I_{mn}^r$, and we give a new proof of the dimension of $R/I_{mn}^r$. We also characterize when the ring $R/I_{mn}^r$ is Gorenstein, thereby answering a question of Li in the toric case. Finally, we give combinatorial descriptions of the facets of the Stanley-Reisner complex of the initial ideal of $I_{mn}^r$ with respect to a diagonal term order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22730 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invariants of toric double determinantal rings Biermann, Jennifer De Negri, Emanuela Gasanova, Oleksandra Musapaşaoğlu, Aslı Roy, Sudeshna Commutative Algebra 05E40 (Primary), 13F65, 14M12 (Secondary) We study a class of double determinantal ideals denoted $I_{mn}^r$, which are generated by minors of size 2, and show that they are equal to the Hibi rings of certain finite distributive lattices. We compute the number of minimal generators of $I_{mn}^r$, as well as the multiplicity, regularity, a-invariant, Hilbert function, and $h$-polynomial of the ring $R/I_{mn}^r$, and we give a new proof of the dimension of $R/I_{mn}^r$. We also characterize when the ring $R/I_{mn}^r$ is Gorenstein, thereby answering a question of Li in the toric case. Finally, we give combinatorial descriptions of the facets of the Stanley-Reisner complex of the initial ideal of $I_{mn}^r$ with respect to a diagonal term order. |
| title | Invariants of toric double determinantal rings |
| topic | Commutative Algebra 05E40 (Primary), 13F65, 14M12 (Secondary) |
| url | https://arxiv.org/abs/2506.22730 |