Positivity of Relative Canonical Bundles of Families of Canonically Polarized Manifolds
نویسنده
چکیده
The Kähler-Einstein metrics on the fibers of an effectively parameterized family of canonically polarized manifolds induce a hermitian metric on the relative canonical bundle. We use a global elliptic equation to show that this metric is strictly positive. Applications concern the curvature of the classical and generalized Weil-Petersson metrics and hyperbolicity of moduli spaces.
منابع مشابه
Positivity of Relative Canonical Bundles for Families of Canonically Polarized Manifolds
Given an effectively parameterized family of canonically polarized manifolds the Kähler-Einstein metrics on the fibers induce a hermitian metric on the relative canonical bundle. We use a global elliptic equation to show that this metric is strictly positive. For degenerating families we obtain a singular hermitian metric. Applications concern the curvature of the classical and generalized Weil...
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