The geometric Shafarevich boundedness conjecture is established for the moduli stack of stable minimal models, including KSB pairs.
Koll´ ar,Moduli of varieties of general type
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abstract
This is a survey paper discussing the moduli problem for varieties of general type.
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2026 2verdicts
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Proves an Arakelov inequality for families of semi-log canonical pairs and derives a volume bound for certain fiber spaces.
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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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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.