Positivity of relative canonical bundles for families of canonically polarized manifolds

Georg Schumacher

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arXiv · 0808.3259

Positivity of relative canonical bundles for families of canonically polarized manifolds

Georg Schumacher

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Abstract

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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Georg Schumacher. 2010-10-19. Positivity of relative canonical bundles for families of canonically polarized manifolds. https://arxiv.org/abs/0808.3259

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