  We study the invariants (in particular, the central invariants) of suitable
Poisson pencils from the point of view of the theory of bi-Hamiltonian
reduction, paying a particular attention to the case where the Poisson pencil
is exact. We show that the exactness is preserved by the reduction. In the
Drinfeld-Sokolov case, the same is true for the characteristic polynomial of
the pencil, which plays a crucial role in the definition of the central
invariants. We also discuss the bi-Hamiltonian structures of a generalized
Drinfeld-Sokolov hierarchy and of the Camassa-Holm equation.
