Cohen-Macaulayness of Powers of Edge Ideals of Weighted Oriented Graphs
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_ | 1866914031458058240 |
|---|---|
| author | Hien, Truong Thi Li, Jiaxin Trung, Tran Nam Zhu, Guangjun |
| author_facet | Hien, Truong Thi Li, Jiaxin Trung, Tran Nam Zhu, Guangjun |
| contents | For the edge ideal $I(\D)$ of a weighted oriented graph $\D$, we prove that its symbolic powers $I(\D)^{(t)}$ are Cohen-Macaulay for all $t\geqslant 1$ if and only if the underlying graph $G$ is composed of a disjoint union of some complete graphs. We also completely characterize the Cohen-Macaulayness of the ordinary powers $I(\D)^t$ for all $t\geqslant 2$. Furthermore, we provide a criterion for determining whether $I(\D)^t=I(\D)^{(t)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08677 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohen-Macaulayness of Powers of Edge Ideals of Weighted Oriented Graphs Hien, Truong Thi Li, Jiaxin Trung, Tran Nam Zhu, Guangjun Commutative Algebra Primary 13C14, 13C05, 13C15, Secondary 05C25, 05E40 For the edge ideal $I(\D)$ of a weighted oriented graph $\D$, we prove that its symbolic powers $I(\D)^{(t)}$ are Cohen-Macaulay for all $t\geqslant 1$ if and only if the underlying graph $G$ is composed of a disjoint union of some complete graphs. We also completely characterize the Cohen-Macaulayness of the ordinary powers $I(\D)^t$ for all $t\geqslant 2$. Furthermore, we provide a criterion for determining whether $I(\D)^t=I(\D)^{(t)}$. |
| title | Cohen-Macaulayness of Powers of Edge Ideals of Weighted Oriented Graphs |
| topic | Commutative Algebra Primary 13C14, 13C05, 13C15, Secondary 05C25, 05E40 |
| url | https://arxiv.org/abs/2509.08677 |