Generalizes the DCC property of Iitaka volumes to real coefficients on usual pairs and establishes it for generalised pairs with natural boundedness assumptions.
Birkar, Moduli of algebraic varieties, arXiv:2211.11237 (2022)
4 Pith papers cite this work. Polarity classification is still indexing.
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The geometric Shafarevich boundedness conjecture is established for the moduli stack of stable minimal models, including KSB pairs.
Algebraically integrable foliations of fixed dimension and bounded adjoint volume are log birationally bounded, which implies birational boundedness for stable families of maximal variation.
Proves an Arakelov inequality for families of semi-log canonical pairs and derives a volume bound for certain fiber spaces.
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On the DCC Property of Iitaka Volume with Real Coefficients and Generalised Pairs
Generalizes the DCC property of Iitaka volumes to real coefficients on usual pairs and establishes it for generalised pairs with natural boundedness assumptions.
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Geometric Shafarevich boundedness conjecture for families of polarized varieties
The geometric Shafarevich boundedness conjecture is established for the moduli stack of stable minimal models, including KSB pairs.
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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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Arakelov inequality for families of pairs
Proves an Arakelov inequality for families of semi-log canonical pairs and derives a volume bound for certain fiber spaces.