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2 results

  • Minimal model program for algebraically integrable foliations on klt varieties

  • Part of
  • Jihao Liu, Fanjun Meng, Lingyao Xie
  • Journal:
    Compositio Mathematica / Volume 161 / Issue 12 / December 2025
    Published online by Cambridge University Press:
    30 March 2026, pp. 3213-3276
    Print publication:
    December 2025
    • Article
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  • For log canonical (lc) algebraically integrable foliations on Kawamata log terminal (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.