Stable Degenerations of log Fano Fibration Germs
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915907855450112 |
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| author | Han, Jiyuan Miao, Minghao Qi, Lu Wang, Linsheng Zhang, Tong |
| author_facet | Han, Jiyuan Miao, Minghao Qi, Lu Wang, Linsheng Zhang, Tong |
| contents | We prove the stable degeneration conjecture of log Fano fibration germs formulated by Sun-Zhang. Precisely, we introduce the $\mathbf{H}$-invariant for filtrations over a log Fano fibration germ, and show that there exists a unique quasi-monomial valuation $v_0$ minimizing the $\mathbf{H}$-invariant. Moreover, we prove that the associated graded ring of $v_0$ is finitely generated and induces a special degeneration to a K-semistable polarized log Fano fibration germ, which further admits a unique K-polystable special degeneration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09269 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stable Degenerations of log Fano Fibration Germs Han, Jiyuan Miao, Minghao Qi, Lu Wang, Linsheng Zhang, Tong Algebraic Geometry Differential Geometry We prove the stable degeneration conjecture of log Fano fibration germs formulated by Sun-Zhang. Precisely, we introduce the $\mathbf{H}$-invariant for filtrations over a log Fano fibration germ, and show that there exists a unique quasi-monomial valuation $v_0$ minimizing the $\mathbf{H}$-invariant. Moreover, we prove that the associated graded ring of $v_0$ is finitely generated and induces a special degeneration to a K-semistable polarized log Fano fibration germ, which further admits a unique K-polystable special degeneration. |
| title | Stable Degenerations of log Fano Fibration Germs |
| topic | Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2603.09269 |