Betti numbers for connected sums of graded Gorenstein artinian algebras
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arXiv
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| Autores principales: | , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910302735433728 |
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| author | Altafi, Nasrin Di Gennaro, Roberta Galetto, Federico Grate, Sean Miro-Roig, Rosa M. Nagel, Uwe Seceleanu, Alexandra Watanabe, Junzo |
| author_facet | Altafi, Nasrin Di Gennaro, Roberta Galetto, Federico Grate, Sean Miro-Roig, Rosa M. Nagel, Uwe Seceleanu, Alexandra Watanabe, Junzo |
| contents | The connected sum construction, which takes as input Gorenstein rings and produces new Gorenstein rings, can be considered as an algebraic analogue for the topological construction having the same name. We determine the graded Betti numbers for connected sums of graded Artinian Gorenstein algebras. Along the way, we find the graded Betti numbers for fiber products of graded rings; an analogous result was obtained in the local case by Geller. We relate the connected sum construction to the doubling construction, which also produces Gorenstein rings. Specifically, we show that a connected sum of doublings is the doubling of a fiber product ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10492 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Betti numbers for connected sums of graded Gorenstein artinian algebras Altafi, Nasrin Di Gennaro, Roberta Galetto, Federico Grate, Sean Miro-Roig, Rosa M. Nagel, Uwe Seceleanu, Alexandra Watanabe, Junzo Commutative Algebra 13D02, 13H10 The connected sum construction, which takes as input Gorenstein rings and produces new Gorenstein rings, can be considered as an algebraic analogue for the topological construction having the same name. We determine the graded Betti numbers for connected sums of graded Artinian Gorenstein algebras. Along the way, we find the graded Betti numbers for fiber products of graded rings; an analogous result was obtained in the local case by Geller. We relate the connected sum construction to the doubling construction, which also produces Gorenstein rings. Specifically, we show that a connected sum of doublings is the doubling of a fiber product ring. |
| title | Betti numbers for connected sums of graded Gorenstein artinian algebras |
| topic | Commutative Algebra 13D02, 13H10 |
| url | https://arxiv.org/abs/2401.10492 |