  In this paper, we compute the dimensions of the 1st and 2nd cohomology groups
of all the pluricanonical bundles for Hirzebruch surfaces, and the dimensions
of the 1st and 2nd cohomology groups of the second pluricanonical bundles for a
blow-up of a projective plane along finite many distinct points. Both of them
give examples showing that the higher cohomology of the pluricanonical bundle
is not deformation invariant.
