Cohen-Macaulayness of vertex splittable monomial ideals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929284514316288 |
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| author | Crupi, Marilena Ficarra, Antonino |
| author_facet | Crupi, Marilena Ficarra, Antonino |
| contents | In this paper, we give a new criterion for the Cohen-Macaulayness of vertex splittable ideals, a family of monomial ideals recently introduced by Moradi and Khosh-Ahang. Our result relies on a Betti splitting of the ideal and provides an inductive way of checking the Cohen-Macaulay property. As a result, we obtain characterizations for Gorenstein, level and pseudo-Gorenstein vertex splittable ideals. Furthermore, we provide new and simpler combinatorial proofs of known Cohen-Macaulay criteria for several families of monomial ideals, such as (vector-spread) strongly stable ideals and (componentwise) polymatroidals. Finally, we characterize the family of bi-Cohen-Macaulay graphs by the novel criterion for the Cohen-Macaulayness of vertex splittable ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14299 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohen-Macaulayness of vertex splittable monomial ideals Crupi, Marilena Ficarra, Antonino Commutative Algebra In this paper, we give a new criterion for the Cohen-Macaulayness of vertex splittable ideals, a family of monomial ideals recently introduced by Moradi and Khosh-Ahang. Our result relies on a Betti splitting of the ideal and provides an inductive way of checking the Cohen-Macaulay property. As a result, we obtain characterizations for Gorenstein, level and pseudo-Gorenstein vertex splittable ideals. Furthermore, we provide new and simpler combinatorial proofs of known Cohen-Macaulay criteria for several families of monomial ideals, such as (vector-spread) strongly stable ideals and (componentwise) polymatroidals. Finally, we characterize the family of bi-Cohen-Macaulay graphs by the novel criterion for the Cohen-Macaulayness of vertex splittable ideals. |
| title | Cohen-Macaulayness of vertex splittable monomial ideals |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2403.14299 |