Point varieties and point-exactness of Koszul algebras
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908889593675776 |
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| author | Hu, Haigang Wu, Wenchao Ye, Yu |
| author_facet | Hu, Haigang Wu, Wenchao Ye, Yu |
| contents | In this paper, we introduce the point-exact condition for a Koszul algebra $A$, which is useful for characterizing the (G1) condition of $A$ in the sense of Mori. Let $B = A/(f)$, where $f \in A_2$ is a regular normal element. We show that if $A$ satisfies the (G1) condition and is point-exact up to degree $\ell \geq 2$, then $B$ also satisfies the (G1) condition and is point-exact up to degree $\ell$. Moreover, we show that skew polynomial algebras satisfy the point-exact condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15385 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Point varieties and point-exactness of Koszul algebras Hu, Haigang Wu, Wenchao Ye, Yu Rings and Algebras 16E65, 16S38, 16W50 In this paper, we introduce the point-exact condition for a Koszul algebra $A$, which is useful for characterizing the (G1) condition of $A$ in the sense of Mori. Let $B = A/(f)$, where $f \in A_2$ is a regular normal element. We show that if $A$ satisfies the (G1) condition and is point-exact up to degree $\ell \geq 2$, then $B$ also satisfies the (G1) condition and is point-exact up to degree $\ell$. Moreover, we show that skew polynomial algebras satisfy the point-exact condition. |
| title | Point varieties and point-exactness of Koszul algebras |
| topic | Rings and Algebras 16E65, 16S38, 16W50 |
| url | https://arxiv.org/abs/2603.15385 |