Minimal model program for algebraically integrable foliations on klt varieties
| Autor: | Liu, Jihao, Meng, Fanjun, Xie, Lingyao |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 with 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. Comment: 56 pages. New results added and expositions improved. We additionally prove the base-point-freeness theorem and the finite generation of polarized canonical rings. As a corollary, we also show that every $\mathbb{Q}$-factorial klt variety with an lc algebraically integrable Fano foliation structure is a Mori dream space |
| Databáze: | arXiv |
| Externí odkaz: |
|