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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.19273 |
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| _version_ | 1866911204514988032 |
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| author | Chen, Zhiyuan |
| author_facet | Chen, Zhiyuan |
| contents | We prove that for a locally stable family of klt singularities with constant local volume, the ideal sequences of the minimizing valuations for the normalized volume function form a family of ideals with flat cosupport, which induces a degeneration to a locally stable family of K-semistable log Fano cone singularities. Our proof is a family version of the method of C. Xu and Z. Zhuang proving finite generation by Kollár models and multiple degenerations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19273 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stable degeneration of families of klt singularities with constant local volume Chen, Zhiyuan Algebraic Geometry We prove that for a locally stable family of klt singularities with constant local volume, the ideal sequences of the minimizing valuations for the normalized volume function form a family of ideals with flat cosupport, which induces a degeneration to a locally stable family of K-semistable log Fano cone singularities. Our proof is a family version of the method of C. Xu and Z. Zhuang proving finite generation by Kollár models and multiple degenerations. |
| title | Stable degeneration of families of klt singularities with constant local volume |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2405.19273 |