The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908803560112128 |
|---|---|
| author | Chau, Trung Erey, Nursel Maithani, Aryaman |
| author_facet | Chau, Trung Erey, Nursel Maithani, Aryaman |
| contents | Every monomial ideal $I$ has a Scarf complex, which is a subcomplex of its minimal free resolution. We say that $I$ is Scarf if its Scarf complex is also its minimal free resolution. In this paper, we fully characterize all pairs $(G,n)$ of a graph $G$ and an integer $n$ such that the squarefree power $I(G)^{[n]}$ or the symbolic power $I(G)^{(n)}$ of the edge ideal $I(G)$ is Scarf. We also determine all graphs $G$ such that its cover ideal $J(G)$ is Scarf, with an explicit description when $G$ is either chordal or bipartite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs Chau, Trung Erey, Nursel Maithani, Aryaman Commutative Algebra Combinatorics 13D02, 13F55, 05C65, 05C75, 05E40 Every monomial ideal $I$ has a Scarf complex, which is a subcomplex of its minimal free resolution. We say that $I$ is Scarf if its Scarf complex is also its minimal free resolution. In this paper, we fully characterize all pairs $(G,n)$ of a graph $G$ and an integer $n$ such that the squarefree power $I(G)^{[n]}$ or the symbolic power $I(G)^{(n)}$ of the edge ideal $I(G)$ is Scarf. We also determine all graphs $G$ such that its cover ideal $J(G)$ is Scarf, with an explicit description when $G$ is either chordal or bipartite. |
| title | The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs |
| topic | Commutative Algebra Combinatorics 13D02, 13F55, 05C65, 05C75, 05E40 |
| url | https://arxiv.org/abs/2503.13337 |