Existence of minimal models for threefold generalized pairs in positive characteristic
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913581676625920 |
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| author | Yang, Tianle Ye, Zelin Zhang, Zhiyao |
| author_facet | Yang, Tianle Ye, Zelin Zhang, Zhiyao |
| contents | Let $\mathbb{K}$ be an algebraically closed field of characteristic $p>5$. We show the existence of minimal models for pseudo-effective NQC lc generalized pairs in dimension three over $\mathbb{K}$. As a consequence, we prove the termination of flips for pseudo-effective threefold NQC lc generalized pairs over $\mathbb{K}$. This provides a new proof on the termination of flips for pseudo-effective pairs over $\mathbb{K}$ without using the non-vanishing theorems. A key ingredient of our proof is the ACC for lc thresholds in dimension $\leq 3$ and the global ACC in dimension $\leq 2$ for generalized pairs over $\mathbb{K}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12269 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of minimal models for threefold generalized pairs in positive characteristic Yang, Tianle Ye, Zelin Zhang, Zhiyao Algebraic Geometry 14E30, 14B05 Let $\mathbb{K}$ be an algebraically closed field of characteristic $p>5$. We show the existence of minimal models for pseudo-effective NQC lc generalized pairs in dimension three over $\mathbb{K}$. As a consequence, we prove the termination of flips for pseudo-effective threefold NQC lc generalized pairs over $\mathbb{K}$. This provides a new proof on the termination of flips for pseudo-effective pairs over $\mathbb{K}$ without using the non-vanishing theorems. A key ingredient of our proof is the ACC for lc thresholds in dimension $\leq 3$ and the global ACC in dimension $\leq 2$ for generalized pairs over $\mathbb{K}$. |
| title | Existence of minimal models for threefold generalized pairs in positive characteristic |
| topic | Algebraic Geometry 14E30, 14B05 |
| url | https://arxiv.org/abs/2408.12269 |