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Minimal model program for algebraically integrable foliations on klt varieties

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arxiv 2404.01559 v3 pith:UKO26J34 submitted 2024-04-02 math.AG math.DS

classification math.AGmath.DS
keywords algebraicallyintegrablefoliationsvarietiesexistenceminimalcasciniflips
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abstract

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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sarkisov program for algebraically integrable and threefold foliations

    math.AG 2025-05 conditional novelty 8.0 of 10

    The authors establish that for algebraically integrable foliations on klt varieties, and for rank one foliations on threefolds, any two Mori fiber spaces are connected by Sarkisov links.

  2. Effective positivity of Hodge bundles and applications

    math.AG 2025-06 conditional novelty 7.0 of 10

    The paper proves effective positivity of Hodge bundles for stable families and derives uniform lower bounds on volumes and automorphism groups, in terms only of dimension and allowed boundary coefficients.

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