The minimal volume of stable surfaces of rank one is determined with uniqueness up to isomorphism, resolving a conjecture of Alexeev and the second author.
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Algebraically integrable foliations of fixed dimension and bounded adjoint volume are log birationally bounded, which implies birational boundedness for stable families of maximal variation.
The normalization of the moduli space of polarized klt good minimal models of arbitrary Kodaira dimension is quasi-projective.
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The minimal volume of stable surfaces of rank one
The minimal volume of stable surfaces of rank one is determined with uniqueness up to isomorphism, resolving a conjecture of Alexeev and the second author.
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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.