On the Hilbert depth of monomial ideals
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915489467334656 |
|---|---|
| author | Balanescu, Silviu Cimpoeas, Mircea Krattenthaler, Christian |
| author_facet | Balanescu, Silviu Cimpoeas, Mircea Krattenthaler, Christian |
| contents | Let $S=K[x_1,\ldots,x_n]$ be the ring of polynomials over a field $K$. Given two monomial ideals $0\subset I\subsetneq J \subset S$, we present a new method to compute the Hilbert depth of $J/I$. As an application, we show that if $u\in S$ is a monomial regular of $S/I$, then $\operatorname{hdepth}(S/I)\geq \operatorname{hdepth}(S/(I,u))\geq \operatorname{hdepth}(S/I)-1.$
Also, we reprove the formula of the Hilbert depth of a squarefree Veronese ideal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09450 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Hilbert depth of monomial ideals Balanescu, Silviu Cimpoeas, Mircea Krattenthaler, Christian Commutative Algebra Combinatorics 05A18, 06A07, 13C15, 13P10, 13F20 Let $S=K[x_1,\ldots,x_n]$ be the ring of polynomials over a field $K$. Given two monomial ideals $0\subset I\subsetneq J \subset S$, we present a new method to compute the Hilbert depth of $J/I$. As an application, we show that if $u\in S$ is a monomial regular of $S/I$, then $\operatorname{hdepth}(S/I)\geq \operatorname{hdepth}(S/(I,u))\geq \operatorname{hdepth}(S/I)-1.$ Also, we reprove the formula of the Hilbert depth of a squarefree Veronese ideal. |
| title | On the Hilbert depth of monomial ideals |
| topic | Commutative Algebra Combinatorics 05A18, 06A07, 13C15, 13P10, 13F20 |
| url | https://arxiv.org/abs/2306.09450 |