Positivity of relative canonical bundles for families of canonically polarized manifolds

Details Positivity of relative canonical bundles for families of canonically polarized manifolds Positivity of relative canonical bundles for families of canonically polarized manifolds

2008-08-25

arxiv.org/abs/0808.3259v4

Mathematics

Complex Variables

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Scientific paper

Given an effectively parameterized family of canonically polarized manifolds the Kaehler-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. Main application is an analytic proof of the quasi-projectivity of the moduli space of canonically polarized manifolds. Further applications in arXiv:1002.4858v2.

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