Algebraically integrable foliations of fixed dimension and bounded adjoint volume are log birationally bounded, which implies birational boundedness for stable families of maximal variation.
Jiao, Boundedness of slc degenerations of polarized log Calabi-Yau pairs, Forum Math
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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.