$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915101213196288 |
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| author | Hu, Zhengyu |
| author_facet | Hu, Zhengyu |
| contents | We develop a theory of $P$-trivial MMP whose each step is $P$-trivial for a given nef divisor $P$. As an application, we prove that, given a projective generalised klt pair $(X,B+M)$ with data $M'$ being just a nef $\mathbb{R}$-divisor, if $K_X+B+M$ birationally has a Nakayama-Zariski decomposition with nef positive part, and either if $M'$ or the positive part is log numerically effective, then it has a minimal model. Furthermore, we prove this for generalised lc pairs in dimension $3$. This is a generalisation of the main theorem of [Birkar-Hu14]. We also prove some related results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Hu, Zhengyu Algebraic Geometry We develop a theory of $P$-trivial MMP whose each step is $P$-trivial for a given nef divisor $P$. As an application, we prove that, given a projective generalised klt pair $(X,B+M)$ with data $M'$ being just a nef $\mathbb{R}$-divisor, if $K_X+B+M$ birationally has a Nakayama-Zariski decomposition with nef positive part, and either if $M'$ or the positive part is log numerically effective, then it has a minimal model. Furthermore, we prove this for generalised lc pairs in dimension $3$. This is a generalisation of the main theorem of [Birkar-Hu14]. We also prove some related results. |
| title | $P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2501.07551 |