  We prove an effective vanishing theorem for direct images of log
pluricanonical bundles of projective semi-log canonical pairs. As an
application, we obtain a semipositivity theorem for direct images of relative
log pluricanonical bundles of projective semi-log canonical pairs over curves,
which implies the projectivity of the moduli spaces of stable varieties. It is
worth mentioning that we do not use the theory of variation of (mixed) Hodge
structure.
