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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.10737 |
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| _version_ | 1866908589048725504 |
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| author | Chen, Zhiyuan |
| author_facet | Chen, Zhiyuan |
| contents | In the algebraic theory of K-stability, one of the most challenging problems is to show the graded algebra associated with certain higher rank quasi-monomial valuations are finitely generated. In the global case of Fano varieties and local case of klt singularities, the finite generation has been proved for quasi-monomial valuations on models of qdlt Fano type. In this paper, we generalize these results using a different argument, by studying the extended Rees algebra via a more algebraic approach. As consequences, our results apply to fibrations of Fano type with singularities worse than qdlt, and graded algebras coming from the multi-section ring of arbitrary divisors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite generation of higher rank quasi-monomial valuations via the extended Rees algebra Chen, Zhiyuan Algebraic Geometry In the algebraic theory of K-stability, one of the most challenging problems is to show the graded algebra associated with certain higher rank quasi-monomial valuations are finitely generated. In the global case of Fano varieties and local case of klt singularities, the finite generation has been proved for quasi-monomial valuations on models of qdlt Fano type. In this paper, we generalize these results using a different argument, by studying the extended Rees algebra via a more algebraic approach. As consequences, our results apply to fibrations of Fano type with singularities worse than qdlt, and graded algebras coming from the multi-section ring of arbitrary divisors. |
| title | Finite generation of higher rank quasi-monomial valuations via the extended Rees algebra |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2510.10737 |