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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.00732 |
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| _version_ | 1866910007489986560 |
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| author | Moriyama, Nao |
| author_facet | Moriyama, Nao |
| contents | We construct a normal projective $\mathbb{Q}$-Gorenstein surface over an algebraically closed field whose canonical ring is not finitely generated. Moreover, we provide a counterexample to the minimal model program for $\mathbb{Q}$-Gorenstein surfaces, which was previously unknown in positive characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00732 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Note on $\mathbb{Q}$-Gorenstein surfaces Moriyama, Nao Algebraic Geometry We construct a normal projective $\mathbb{Q}$-Gorenstein surface over an algebraically closed field whose canonical ring is not finitely generated. Moreover, we provide a counterexample to the minimal model program for $\mathbb{Q}$-Gorenstein surfaces, which was previously unknown in positive characteristic. |
| title | A Note on $\mathbb{Q}$-Gorenstein surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2602.00732 |