DescriptionLet V be a finite dimensional complex vector space, V^∗ its dual, and let X ⊂ P(V ) be a smooth projective variety of dimension n and degree d ≥ 2. For a generic n−tuple of hyperplanes (H_1, ..., H_n) ∈ P(V^∗)^n, the intersection X ∩ H_1 ∩ · · · ∩ H_n consists of d distinct points. We define the “discriminant of X” to be the set D_X of n-tuples for which the set-theoretic intersection is not equal to d points. Then D_X ⊂ P(V^∗)^n is a hypersurface 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⟩ where K is the canonical line bundle of X and L → X is the restriction of the hyperplane bundle. As a corollary, we obtain a generalization of Paul’s formula [14] which relates the Mabuchi K-energy on the space of Bergman metrics to ∆X, the “hyperdiscriminant of X”.