The volume intrinsic to a commutative graded algebra
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913433262227456 |
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| author | Adiprasito, Karim Alexander Papadakis, Stavros Argyrios Petrotou, Vasiliki |
| author_facet | Adiprasito, Karim Alexander Papadakis, Stavros Argyrios Petrotou, Vasiliki |
| contents | Recent works of the authors have demonstrated the usefulness of considering moduli spaces of Artinian reductions of a given ring when studying standard graded rings and their Lefschetz properties. This paper illuminates a key aspect of these works, the behaviour of the canonical module under deformations in this moduli space. We demonstrate that even when there is no natural geometry around, we can give a viewpoint that behaves like it, effectively constructing geometry out of nothing, giving interpretation to intersection numbers without cycles. Moreover, we explore some properties of this normalization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11916 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The volume intrinsic to a commutative graded algebra Adiprasito, Karim Alexander Papadakis, Stavros Argyrios Petrotou, Vasiliki Commutative Algebra Algebraic Geometry Combinatorics Primary: 13H10, Secondary: 14A05, 05E40, 05E45, Recent works of the authors have demonstrated the usefulness of considering moduli spaces of Artinian reductions of a given ring when studying standard graded rings and their Lefschetz properties. This paper illuminates a key aspect of these works, the behaviour of the canonical module under deformations in this moduli space. We demonstrate that even when there is no natural geometry around, we can give a viewpoint that behaves like it, effectively constructing geometry out of nothing, giving interpretation to intersection numbers without cycles. Moreover, we explore some properties of this normalization. |
| title | The volume intrinsic to a commutative graded algebra |
| topic | Commutative Algebra Algebraic Geometry Combinatorics Primary: 13H10, Secondary: 14A05, 05E40, 05E45, |
| url | https://arxiv.org/abs/2407.11916 |