  For any semisimple Frobenius manifold, we prove that a tau-symmetric
bihamiltonian deformation of its Principal Hierarchy admits an infinite family
of linearizable Virasoro symmetries if and only if all the central invariants
of the corresponding deformation of the bihamiltonian structure are equal to
$\frac{1}{24}$. As an important application of this result, we prove that the
Dubrovin-Zhang hierarchy associated with the semisimple Frobenius manifold
possesses a bihamiltonian structure which can be represented in terms of
differential polynomials.
