A linear generalization of the nearly Gorenstein property, with applications to Veronese subalgebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909986920071168 |
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| author | Miyashita, Sora |
| author_facet | Miyashita, Sora |
| contents | We studies the nearly Gorenstein property for Veronese subalgebras of (semi-)standard graded algebras. We introduce a condition~$(\natural)$ for Cohen--Macaulay semi-standard graded rings, motivated by the study of Ehrhart rings. We show that if a semi-standard graded algebra \( R \) satisfies~$(\natural)$, then its Veronese subalgebras \( R^{(k)} \) are nearly Gorenstein for all sufficiently large \( k \). We also prove that if a standard graded algebra $R$ is nearly Gorenstein so does its Veronese subalgebra $R^{(k)}$ for all $k>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05629 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A linear generalization of the nearly Gorenstein property, with applications to Veronese subalgebras Miyashita, Sora Commutative Algebra Primary 13H10, 05E40, 13A02, Secondary 14M25 We studies the nearly Gorenstein property for Veronese subalgebras of (semi-)standard graded algebras. We introduce a condition~$(\natural)$ for Cohen--Macaulay semi-standard graded rings, motivated by the study of Ehrhart rings. We show that if a semi-standard graded algebra \( R \) satisfies~$(\natural)$, then its Veronese subalgebras \( R^{(k)} \) are nearly Gorenstein for all sufficiently large \( k \). We also prove that if a standard graded algebra $R$ is nearly Gorenstein so does its Veronese subalgebra $R^{(k)}$ for all $k>0$. |
| title | A linear generalization of the nearly Gorenstein property, with applications to Veronese subalgebras |
| topic | Commutative Algebra Primary 13H10, 05E40, 13A02, Secondary 14M25 |
| url | https://arxiv.org/abs/2407.05629 |