Minimal model program on the generic fiber of log Calabi-Yau type fibration
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918242925150208 |
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| author | Kim, Donghyeon Lee, Dae-Won |
| author_facet | Kim, Donghyeon Lee, Dae-Won |
| contents | We study the minimal model program on the geometric generic fiber of a fibration $f:X\to S$ such that for a Zariski dense subset $S'\subseteq S$, $X_s$ is an $\varepsilon$-lc log Calabi--Yau type for every $s\in S'$. We prove that for a fibration $f:X\to S$ of varieties, if the fibers are of $\varepsilon$-lc log Calabi--Yau type, then the geometric generic fiber $X_{\overlineη}$ is pklt. In particular, for any big divisor $D$ on $X_{\overlineη}$, we can run the anticanonical MMP and $D$-MMP with scaling of an ample divisor on $X_{\overlineη}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02429 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal model program on the generic fiber of log Calabi-Yau type fibration Kim, Donghyeon Lee, Dae-Won Algebraic Geometry 14E05, 14E30 We study the minimal model program on the geometric generic fiber of a fibration $f:X\to S$ such that for a Zariski dense subset $S'\subseteq S$, $X_s$ is an $\varepsilon$-lc log Calabi--Yau type for every $s\in S'$. We prove that for a fibration $f:X\to S$ of varieties, if the fibers are of $\varepsilon$-lc log Calabi--Yau type, then the geometric generic fiber $X_{\overlineη}$ is pklt. In particular, for any big divisor $D$ on $X_{\overlineη}$, we can run the anticanonical MMP and $D$-MMP with scaling of an ample divisor on $X_{\overlineη}$. |
| title | Minimal model program on the generic fiber of log Calabi-Yau type fibration |
| topic | Algebraic Geometry 14E05, 14E30 |
| url | https://arxiv.org/abs/2512.02429 |