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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.07829 |
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| _version_ | 1866929675064836096 |
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| author | Meng, Cheng |
| author_facet | Meng, Cheng |
| contents | In this paper, we prove that if $P$ is a homogeneous prime ideal inside a standard graded polynomial ring $S$ with $\dim(S/P)=d$, and for $s \leq d$, adjoining $s$ general linear forms to the prime ideal changes the $(d-s)$-th Hilbert coefficient by 1, then $\text{depth}(S/P)=s-1$. This criterion also tells us about possible restrictions on the generic initial ideal of a prime ideal inside a polynomial ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07829 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Restrictions on Hilbert coefficients give depths of graded domains Meng, Cheng Commutative Algebra 13P10 In this paper, we prove that if $P$ is a homogeneous prime ideal inside a standard graded polynomial ring $S$ with $\dim(S/P)=d$, and for $s \leq d$, adjoining $s$ general linear forms to the prime ideal changes the $(d-s)$-th Hilbert coefficient by 1, then $\text{depth}(S/P)=s-1$. This criterion also tells us about possible restrictions on the generic initial ideal of a prime ideal inside a polynomial ring. |
| title | Restrictions on Hilbert coefficients give depths of graded domains |
| topic | Commutative Algebra 13P10 |
| url | https://arxiv.org/abs/2501.07829 |