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The Shafarevich conjecture revisited: Finiteness of pointed families of polarized varieties
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Motivated by Lang-Vojta's conjectures on hyperbolic varieties, we prove a new version of the Shafarevich conjecture in which we establish the finiteness of pointed families of polarized varieties. We then give an arithmetic application to the finiteness of integral points on moduli spaces of polarized varieties.
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Stratified Hyperbolicity of the moduli stack of stable minimal models, II: Big Picard Theorem and the stratified Brody hyperbolicity
Every stratum in a birationally admissible stratification of Birkar's moduli stack of stable minimal models is Picard hyperbolic, Borel hyperbolic, and Brody hyperbolic.
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