  In this paper we will discuss some features of the bihamiltonian method for
solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and
make contact with the theory of Algebraic Complete Integrability and,
specifically, with the Veselov--Novikov notion of algebro-geometric (AG)
Poisson brackets. The "bihamiltonian" method for separating the Hamilton-Jacobi
equations is based on the notion of pencil of Poisson brackets and on the
Gel'fand-Zakharevich (GZ) approach to integrable systems. We will herewith show
how, quite naturally, GZ systems may give rise to AG Poisson brackets, together
with specific recipes to solve the H-J equations. We will then show how this
setting works by framing results by Veselov and Penskoi about the algebraic
integrability of the Volterra lattice within the bihamiltonian setting for
Separation of Variables.
