Generalizes the DCC property of Iitaka volumes to real coefficients on usual pairs and establishes it for generalised pairs with natural boundedness assumptions.
Singularities on Fano fibrations and beyond
5 Pith papers cite this work. Polarity classification is still indexing.
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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.
Constructs smooth projective Calabi-Yau varieties in every dimension with doubly exponentially growing index and Betti numbers, conjectured maximal.
Proves existence of numerically good minimal models for generalized klt pairs of relative log numerical dimension zero assuming Generalized Nonvanishing via a numerical generalized canonical bundle formula.
The normalization of the moduli space of polarized klt good minimal models of arbitrary Kodaira dimension is quasi-projective.
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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.