  We address the problem of classifying discrete differential-geometric Poisson
brackets (dDGPBs) of any fixed order on target space of dimension 1. It is
proved that these Poisson brackets (PBs) are in one-to-one correspondence with
the intersection points of certain projective hypersurfaces. In addition, they
can be reduced to cubic PB of standard Volterra lattice by discrete Miura-type
transformations. Finally, improving a consolidation lattice procedure, we
obtain new families of non-degenerate, vector-valued and first order dDGPBs,
which can be considered in the framework of admissible Lie-Poisson group
theory.
