Minimal primes and radicality of ideals generated by adjacent 2-minors
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917169448615936 |
|---|---|
| author | Hibi, Takayuki Navarra, Francesco Qureshi, Ayesha Asloob Madani, Sara Saeedi |
| author_facet | Hibi, Takayuki Navarra, Francesco Qureshi, Ayesha Asloob Madani, Sara Saeedi |
| contents | In this paper, we provide a complete description of the minimal primes of ideals generated by adjacent $2$-minors, in terms of the so-called admissible sets and associated lattice ideals. We prove that for these ideals, the properties of being unmixed, Cohen-Macaulay, level, Gorenstein, and complete intersection are equivalent. Moreover, we give a combinatorial characterization of all convex collections of cells satisfying any of these equivalent properties. Finally, we study the radicality of these ideals and derive necessary combinatorial conditions based on minimal non-radical configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21449 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal primes and radicality of ideals generated by adjacent 2-minors Hibi, Takayuki Navarra, Francesco Qureshi, Ayesha Asloob Madani, Sara Saeedi Commutative Algebra Combinatorics 05B50, 05E40, 13F20, 13P10 In this paper, we provide a complete description of the minimal primes of ideals generated by adjacent $2$-minors, in terms of the so-called admissible sets and associated lattice ideals. We prove that for these ideals, the properties of being unmixed, Cohen-Macaulay, level, Gorenstein, and complete intersection are equivalent. Moreover, we give a combinatorial characterization of all convex collections of cells satisfying any of these equivalent properties. Finally, we study the radicality of these ideals and derive necessary combinatorial conditions based on minimal non-radical configurations. |
| title | Minimal primes and radicality of ideals generated by adjacent 2-minors |
| topic | Commutative Algebra Combinatorics 05B50, 05E40, 13F20, 13P10 |
| url | https://arxiv.org/abs/2512.21449 |