  We establish a new representation of the infinite hierarchy of Pois- son
brackets (PB) for the open Toda lattice in terms of its spectral curve. For the
classical Poisson bracket (PB) we give a representation in the form of a
contour integral of some special Abelian differential (meromorphic one-form) on
the spectral curve. All higher brackets of the infinite hierarchy are obtained
by multiplication of the one-form by a power of the spectral parameter.
