Minimal model program for algebraically integrable foliations on klt varieties

2024/04/02 by Jihao Liu, Fanjun Meng, Liu, Jihao +3 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #14E30 #37F75 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.01559

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 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.

Citations

• Codimension 1 foliations with numerically trivial canonical class on singular spaces

Cited by

• Volumes of foliations birationally bounded by algebraically integrable families
• Variation of algebraically integrable adjoint foliated structures
• Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures
• MMP for generalized foliated threefolds of rank one

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• MMP for algebraically integrable foliations
• Flop between algebraically integrable foliations on potentially klt varieties
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• Minimal model program for algebraically integrable adjoint foliated structures
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