  Let X be a smooth, linearly normal algebraic variety. It is shown that the
Mabuchi energy of X restricted to the Bergman metrics is completely determined
by the X-hyperdiscriminant of format (n-1) and the Chow form of X. As a
corollary it is shown that the Mabuchi energy is bounded from below for all
degenerations in G if and only if the hyperdiscriminant polytope dominates the
Chow polytope for all maximal algebraic tori H of G .
