Betti cones over fibre products
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909166605434880 |
|---|---|
| author | Ananthnarayan, H. Javadekar, Omkar Kumar, Rajiv |
| author_facet | Ananthnarayan, H. Javadekar, Omkar Kumar, Rajiv |
| contents | Let $R$ be a fibre product of standard graded algebras over a field. We study the structure of syzygies of finitely generated graded $R$-modules. As an application of this, we show that the existence of an $R$-module of finite regularity and infinite projective dimension forces $R$ to be Koszul. We also look at the extremal rays of the Betti cone of finitely generated graded $R$-modules, and show that when $\operatorname{depth}(R)=1$, they are spanned by the Betti tables of pure $R$-modules if and only if $R$ is Cohen-Macaulay with minimal multiplicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07297 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Betti cones over fibre products Ananthnarayan, H. Javadekar, Omkar Kumar, Rajiv Commutative Algebra 13A02, 13D02, 13D40 Let $R$ be a fibre product of standard graded algebras over a field. We study the structure of syzygies of finitely generated graded $R$-modules. As an application of this, we show that the existence of an $R$-module of finite regularity and infinite projective dimension forces $R$ to be Koszul. We also look at the extremal rays of the Betti cone of finitely generated graded $R$-modules, and show that when $\operatorname{depth}(R)=1$, they are spanned by the Betti tables of pure $R$-modules if and only if $R$ is Cohen-Macaulay with minimal multiplicity. |
| title | Betti cones over fibre products |
| topic | Commutative Algebra 13A02, 13D02, 13D40 |
| url | https://arxiv.org/abs/2404.07297 |