Multiplicity of powers of squarefree monomial ideals
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913570501951488 |
|---|---|
| author | Thuy, Phan Thi Vu, Thanh |
| author_facet | Thuy, Phan Thi Vu, Thanh |
| contents | Let $I$ be an arbitrary nonzero squarefree monomial ideal of dimension $d$ in a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_n]$. Let $μ$ be the number of associated primes of $S/I$ of dimension $d$. We prove that the multiplicity of powers of $I$ is given by
$$e_0(S/I^s) = μ\binom{n-d+s-1}{s-1},$$
for all $s \ge 1$. Consequently, we compute the multiplicity of all powers of path ideals of cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiplicity of powers of squarefree monomial ideals Thuy, Phan Thi Vu, Thanh Commutative Algebra 13H15, 05E40, 13F55 Let $I$ be an arbitrary nonzero squarefree monomial ideal of dimension $d$ in a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_n]$. Let $μ$ be the number of associated primes of $S/I$ of dimension $d$. We prove that the multiplicity of powers of $I$ is given by $$e_0(S/I^s) = μ\binom{n-d+s-1}{s-1},$$ for all $s \ge 1$. Consequently, we compute the multiplicity of all powers of path ideals of cycles. |
| title | Multiplicity of powers of squarefree monomial ideals |
| topic | Commutative Algebra 13H15, 05E40, 13F55 |
| url | https://arxiv.org/abs/2411.01287 |