Relative stability theory and properness of K-moduli spaces
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866918155966742528 |
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| author | Blum, Harold Liu, Yuchen Xu, Chenyang Zhuang, Ziquan |
| author_facet | Blum, Harold Liu, Yuchen Xu, Chenyang Zhuang, Ziquan |
| contents | We define the relative stability threshold of a family of Fano varieties over a DVR and show that it is computed by a divisorial valuation. In the case when the special fiber is K-unstable, but the generic fiber is K-semistable, we use the divisorial valuation computing the threshold to replace the special fiber by a new one with a strictly larger stability threshold. Iterating this process yields a new and more direct proof of the properness of the K-moduli space that uses only birational geometry arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06197 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative stability theory and properness of K-moduli spaces Blum, Harold Liu, Yuchen Xu, Chenyang Zhuang, Ziquan Algebraic Geometry 14J45, 14J10, 14E30 We define the relative stability threshold of a family of Fano varieties over a DVR and show that it is computed by a divisorial valuation. In the case when the special fiber is K-unstable, but the generic fiber is K-semistable, we use the divisorial valuation computing the threshold to replace the special fiber by a new one with a strictly larger stability threshold. Iterating this process yields a new and more direct proof of the properness of the K-moduli space that uses only birational geometry arguments. |
| title | Relative stability theory and properness of K-moduli spaces |
| topic | Algebraic Geometry 14J45, 14J10, 14E30 |
| url | https://arxiv.org/abs/2510.06197 |