Algebraically integrable foliations of fixed dimension and bounded adjoint volume are log birationally bounded, which implies birational boundedness for stable families of maximal variation.
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The normalization of the moduli space of polarized klt good minimal models of arbitrary Kodaira dimension is quasi-projective.
The paper reviews progress on the minimal model program for foliations, including singularities, adjunction, MMP on surfaces, and flips on threefolds.
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Birational boundedness of stable families
Algebraically integrable foliations of fixed dimension and bounded adjoint volume are log birationally bounded, which implies birational boundedness for stable families of maximal variation.
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Quasi-Projective Moduli for Polarized klt Good Minimal Models
The normalization of the moduli space of polarized klt good minimal models of arbitrary Kodaira dimension is quasi-projective.
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Recent progress on the Minimal Model Program for foliations
The paper reviews progress on the minimal model program for foliations, including singularities, adjunction, MMP on surfaces, and flips on threefolds.