A family of simplicial resolutions which are DG-algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909445623119872 |
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| author | Cameron, James Chau, Trung Maitra, Sarasij Tribone, Tim |
| author_facet | Cameron, James Chau, Trung Maitra, Sarasij Tribone, Tim |
| contents | Each monomial ideal over a polynomial ring admits a free resolution which has the structure of a DG-algebra, namely, the Taylor resolution. A pivot resolution of a monomial ideal, which we introduce, is a resolution that is always shorter than the Taylor resolution (unless the Taylor resolution is as short as possible) but still retains a DG-algebra structure. We study the basic properties of this family of resolutions including a characterization of when the construction is minimal. Following the work of Sobieska, we use the explicit nature of pivot resolutions to give formulae for the Eisenbud-Shamash construction of a free resolution of a given monomial ideal over complete intersections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_21120 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A family of simplicial resolutions which are DG-algebras Cameron, James Chau, Trung Maitra, Sarasij Tribone, Tim Commutative Algebra Primary: 13D02, 05E40, Secondary: 16W50, 13F55 Each monomial ideal over a polynomial ring admits a free resolution which has the structure of a DG-algebra, namely, the Taylor resolution. A pivot resolution of a monomial ideal, which we introduce, is a resolution that is always shorter than the Taylor resolution (unless the Taylor resolution is as short as possible) but still retains a DG-algebra structure. We study the basic properties of this family of resolutions including a characterization of when the construction is minimal. Following the work of Sobieska, we use the explicit nature of pivot resolutions to give formulae for the Eisenbud-Shamash construction of a free resolution of a given monomial ideal over complete intersections. |
| title | A family of simplicial resolutions which are DG-algebras |
| topic | Commutative Algebra Primary: 13D02, 05E40, Secondary: 16W50, 13F55 |
| url | https://arxiv.org/abs/2412.21120 |