  We discuss, in the framework of Dubrovin-Zhang's perturbative approach to
integrable evolutionary PDEs in 1+1 dimensions, the role of a special class of
Poisson pencils, called exact Poisson pencils. In particular we show that, in
the semisimple case, exactness of the pencil is equivalent to the constancy of
the so-called "central invariants" of the theory that were introduced by
Dubrovin, Liu and Zhang.
