Minimal model program for algebraically integrable foliations on klt varieties
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908395580162048 |
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| author | Liu, Jihao Meng, Fanjun Xie, Lingyao |
| author_facet | Liu, Jihao Meng, Fanjun Xie, Lingyao |
| contents | For lc algebraically integrable foliations on klt varieties, we prove the base-point-freeness theorem, the contraction theorem, and the existence of flips. The first result resolves a conjecture of Cascini and Spicer, while the latter two results strengthen a result of Cascini and Spicer by removing their assumption on the termination of flips.
Moreover, we prove the existence of the minimal model program for lc algebraically integrable foliations on klt varieties and the existence of good minimal models or Mori fiber spaces for lc algebraically integrable foliations polarized by ample divisors on klt varieties. As a consequence, we show that $\mathbb{Q}$-factorial klt varieties with lc algebraically integrable Fano foliation structures are Mori dream spaces. We also show the existence of a Shokurov-type polytope for lc algebraically integrable foliations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal model program for algebraically integrable foliations on klt varieties Liu, Jihao Meng, Fanjun Xie, Lingyao Algebraic Geometry Dynamical Systems 14E30, 37F75 For lc algebraically integrable foliations on klt varieties, we prove the base-point-freeness theorem, the contraction theorem, and the existence of flips. The first result resolves a conjecture of Cascini and Spicer, while the latter two results strengthen a result of Cascini and Spicer by removing their assumption on the termination of flips. Moreover, we prove the existence of the minimal model program for lc algebraically integrable foliations on klt varieties and the existence of good minimal models or Mori fiber spaces for lc algebraically integrable foliations polarized by ample divisors on klt varieties. As a consequence, we show that $\mathbb{Q}$-factorial klt varieties with lc algebraically integrable Fano foliation structures are Mori dream spaces. We also show the existence of a Shokurov-type polytope for lc algebraically integrable foliations. |
| title | Minimal model program for algebraically integrable foliations on klt varieties |
| topic | Algebraic Geometry Dynamical Systems 14E30, 37F75 |
| url | https://arxiv.org/abs/2404.01559 |