  Let V be a finite dimensional complex vector space and V^* its dual and let X
in P(V) be a smooth projective variety of dimension n and degree d at least
two. For a generic n-tuple of hyperplanes H_1,...,H_n in P(V^*)^n, the
intersection of X with H_1,...,H_n consists of d distinct points. We define the
"discriminant of X", to be the the set D(X) of n-tuples for which the
set-theoretic intersection is not equal to d points. Then D(X) is a hyper
surface in P(V^*)^n and the set of defining polynomials, which is a
one-dimensional vector space, is called the "discriminant line". We show that
this line is canonically isomorphic to the Deligne pairing <KL^n,L,...,L> where
K is the canonical line bundle of X and L is the restriction of the hyperplane
bundle to X. As a corollary, we obtain a generalization of Paul"s formula which
relates the Mabuchi K-energy on the space of Bergman metrics to \Delta(X), the
"hyperdiscriminant of X".
