Curvature properties for moduli of canonically polarized manifolds -- an analogy to moduli of Calabi-Yau manifolds (Q467693)

The author studies the analogy between the moduli of canonically polarized varieties and Calabi-Yau manifolds, when these are equipped with Kähler-Einstein forms. Due to the absence of a Torelli-type theorem, the author constructs a Finsler metric in the orbifold sense. Among other things, the author produces a stronger inequality from the curvature formula which yields the negativity of the Finsler metric. This, in turn, implies a Kobayashi hyperbolicity of the moduli stack of canonically polarized varieties.