On the monotonicity of the Hilbert functions for 4-generated pseudo-symmetric monomial curves
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929428059127808 |
|---|---|
| author | Şahin, Nil |
| author_facet | Şahin, Nil |
| contents | In this article we solve the conjecture "Hilbert function of the local ring for a 4 generated pseudo-symmetric numerical semigroup $\langle n_1,n_2,n_3,n_4 \rangle$ is always non-decreasing when $ n_1 < n_2 < n_3 < n_4$". We give a complete characterization to the standard bases when the tangent cone is not Cohen-Macaulay by showing that the number of elements in the standard basis depends on some parameters $s_j$ 's we define. Since the tangent cone is not Cohen-Macaulay, non-decreasingness of the Hilbert fuction was not guaranteed, we proved the non-decreasingness from our explicit Hilbert Function computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09356 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the monotonicity of the Hilbert functions for 4-generated pseudo-symmetric monomial curves Şahin, Nil Commutative Algebra 13H10, 14H20 In this article we solve the conjecture "Hilbert function of the local ring for a 4 generated pseudo-symmetric numerical semigroup $\langle n_1,n_2,n_3,n_4 \rangle$ is always non-decreasing when $ n_1 < n_2 < n_3 < n_4$". We give a complete characterization to the standard bases when the tangent cone is not Cohen-Macaulay by showing that the number of elements in the standard basis depends on some parameters $s_j$ 's we define. Since the tangent cone is not Cohen-Macaulay, non-decreasingness of the Hilbert fuction was not guaranteed, we proved the non-decreasingness from our explicit Hilbert Function computation. |
| title | On the monotonicity of the Hilbert functions for 4-generated pseudo-symmetric monomial curves |
| topic | Commutative Algebra 13H10, 14H20 |
| url | https://arxiv.org/abs/2302.09356 |