Birationally admissible families of stable minimal models with maximal variation have log general type bases, yielding stratified hyperbolicity of the KSBA moduli stack.
Alexeev, Complete moduli in the presence of semiabelian group action , Ann
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Stratified Hyperbolicity of the moduli stack of stable minimal models, I
Birationally admissible families of stable minimal models with maximal variation have log general type bases, yielding stratified hyperbolicity of the KSBA moduli stack.