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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2026 2verdicts
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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.
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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.