Proves Shokurov's global index conjecture for foliations on varieties of dimension at most three.
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The optimal constant in the bend-and-break inequality for foliations of rank r on normal projective varieties is r+1.
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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Shokurov's global index conjecture for threefold foliations
Proves Shokurov's global index conjecture for foliations on varieties of dimension at most three.
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Optimal bend-and-break for foliations
The optimal constant in the bend-and-break inequality for foliations of rank r on normal projective varieties is r+1.
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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.