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A Finsler metric, whose holomorphic curvature is bounded from above by anegative constant, is constructed on the moduli stack of canonically polarizedmanifolds including singularities. Demailly's version of Ahlfors' lemma yieldshyperbolicity of the moduli stack.

Moduli of canonically polarized manifolds, higher order Kodaira-Spencer maps, and an analogy to Calabi-Yau manifolds