Existence of the minimal model program for log canonical generalized pairs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915833033261056 |
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| author | Hu, Zhengyu Liu, Jihao |
| author_facet | Hu, Zhengyu Liu, Jihao |
| contents | We introduce linearly decomposable (LD) generalized pairs, which serve as a workable substitute for rational decompositions in the non-NQC setting. Using LD generalized pairs, together with a refinement of special termination and Kollár-type gluing theory, we prove the existence of flips for log canonical generalized pairs without assuming the klt condition, the NQC condition, or $\mathbb Q$-factoriality. Together with the cone and contraction theorems, this yields the existence of the minimal model program for arbitrary log canonical generalized pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03817 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of the minimal model program for log canonical generalized pairs Hu, Zhengyu Liu, Jihao Algebraic Geometry 14E30, 14B05, 14E05, 14E15 We introduce linearly decomposable (LD) generalized pairs, which serve as a workable substitute for rational decompositions in the non-NQC setting. Using LD generalized pairs, together with a refinement of special termination and Kollár-type gluing theory, we prove the existence of flips for log canonical generalized pairs without assuming the klt condition, the NQC condition, or $\mathbb Q$-factoriality. Together with the cone and contraction theorems, this yields the existence of the minimal model program for arbitrary log canonical generalized pairs. |
| title | Existence of the minimal model program for log canonical generalized pairs |
| topic | Algebraic Geometry 14E30, 14B05, 14E05, 14E15 |
| url | https://arxiv.org/abs/2603.03817 |