  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.
