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The main result of this note is an effective uniform bound for the number ofdeformation types of certain nonisotrivial families of canonically polarizedmanifolds. It extends the author's earlier such bound for the classicalShafarevich Conjecture over function fields to the case of higher dimensionalfibers, but without the disadvantageous iterated use of Chow or Hilbertvarieties that was the core of the proofs in the earlier approaches.

Uniformly effective boundedness of Shafarevich Conjecture-type for families of canonically polarized manifolds