Remarks on the existence of minimal models of log canonical generalized pairs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914044916531200 |
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| author | Tsakanikas, Nikolaos Xie, Lingyao |
| author_facet | Tsakanikas, Nikolaos Xie, Lingyao |
| contents | Given an NQC log canonical generalized pair $(X,B+M)$ whose underlying variety $X$ is not necessarily $\mathbb{Q}$-factorial, we show that one may run a $(K_X+B+M)$-MMP with scaling of an ample divisor which terminates, provided that $(X,B+M)$ has a minimal model in a weaker sense or that $K_X+B+M$ is not pseudo-effective. We also prove the existence of minimal models of pseudo-effective NQC log canonical generalized pairs under various additional assumptions, for instance, when the boundary contains an ample divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09186 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Remarks on the existence of minimal models of log canonical generalized pairs Tsakanikas, Nikolaos Xie, Lingyao Algebraic Geometry 14E30 Given an NQC log canonical generalized pair $(X,B+M)$ whose underlying variety $X$ is not necessarily $\mathbb{Q}$-factorial, we show that one may run a $(K_X+B+M)$-MMP with scaling of an ample divisor which terminates, provided that $(X,B+M)$ has a minimal model in a weaker sense or that $K_X+B+M$ is not pseudo-effective. We also prove the existence of minimal models of pseudo-effective NQC log canonical generalized pairs under various additional assumptions, for instance, when the boundary contains an ample divisor. |
| title | Remarks on the existence of minimal models of log canonical generalized pairs |
| topic | Algebraic Geometry 14E30 |
| url | https://arxiv.org/abs/2301.09186 |