Algebraically integrable foliations of fixed dimension and bounded adjoint volume are log birationally bounded, which implies birational boundedness for stable families of maximal variation.
Moduli of Boundary Polarized
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The normalization of the moduli space of polarized klt good minimal models of arbitrary Kodaira dimension is quasi-projective.
Proves generalized canonical bundle formula for lc-trivial fibrations without nef part assumption in complex analytic setting, plus algebraic counterpart.
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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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Addendum: On generalized canonical bundle formula and boundedness of complements in complex analytic setting
Proves generalized canonical bundle formula for lc-trivial fibrations without nef part assumption in complex analytic setting, plus algebraic counterpart.