Betti numbers of normal edge rings (\bf{I})
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913814294822912 |
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| author | Wang, Zexin Lu, Dancheng |
| author_facet | Wang, Zexin Lu, Dancheng |
| contents | We introduce a novel approach named the {\it induced-subgraph approach} for investigating the Betti numbers of normal edge rings. Utilizing this approach, we compute all the multi-graded Betti numbers of the edge rings associated with two-ear graphs (Definition 4.1) and compact graphs (Definition 5.1). In particular, we show that for two-ear graphs and compact graphs of type 1 or 2, their multi-graded Betti numbers are always equal to the top multi-graded Betti numbers of some of their induced subgraphs. In contrast, some of the multi-graded Betti numbers of compact graphs of type 3 are not the top multi-graded Betti numbers of any of their induced subgraph. We speculate that our approach can be applicable to many other normal edge rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10672 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Betti numbers of normal edge rings (\bf{I}) Wang, Zexin Lu, Dancheng Commutative Algebra 13A02(Primary) 05E40(Secondary) We introduce a novel approach named the {\it induced-subgraph approach} for investigating the Betti numbers of normal edge rings. Utilizing this approach, we compute all the multi-graded Betti numbers of the edge rings associated with two-ear graphs (Definition 4.1) and compact graphs (Definition 5.1). In particular, we show that for two-ear graphs and compact graphs of type 1 or 2, their multi-graded Betti numbers are always equal to the top multi-graded Betti numbers of some of their induced subgraphs. In contrast, some of the multi-graded Betti numbers of compact graphs of type 3 are not the top multi-graded Betti numbers of any of their induced subgraph. We speculate that our approach can be applicable to many other normal edge rings. |
| title | Betti numbers of normal edge rings (\bf{I}) |
| topic | Commutative Algebra 13A02(Primary) 05E40(Secondary) |
| url | https://arxiv.org/abs/2404.10672 |