  An explicit seminorm $||f||_{#}$ on the vector space of Chow vectors of
projective varieties is introduced, and shown to be a generalized Mabuchi
energy functional for Chow varieties. The singularities of the Chow varieties
give rise to currents supported on their singular loci, while the regular parts
are shown to reproduce the Mabuchi energy functional of the corresponding
projective variety. Thus the boundedness from below of the Mabuchi functional,
and hence the existence of K\"ahler-Einstein metrics, is related to the
behavior of the current $[Y_s]$ and the seminorm $||f||_{#}$ along the orbits
of $SL(N+1,{\bf C})$.
