  The following conjecture on the deformation invariance of plurigenera is
proved. For a smooth projective holomorphic family of compact complex manifolds
over the open unit 1-disk such that all the fibers are of general type, every
plurigenus of the fiber is independent of the fiber.
  The proof uses Nadel's multiplier ideal sheaves, Skoda's result on the
generation of ideals with L2 estimates with respect to a plurisubharmonic
weight, and the extension theorem of Ohsawa-Takegoshi-Manivel for holomorphic
top-degree forms which are L2 with respect to a plurisubharmonic weight.
