American Journal of Mathematics

This addendum uses Bloch's original technique of ordinary differential equations to circumvent a difficulty in the proof of Lemma 2 in the paper in the title. This technique at the same time yields the following stronger Nevanlinna's Second Main Theorem with truncation at an order given explicitly by the Chern class of the divisor. For an ample divisor D in an abelian variety A of complex dimension n and for any holomorphic map f: C → A whose image is not contained in any translate of D, the characteristic function of f for D is dominated by the counting function of f for D truncated at order k_n plus an error term of logarithmic order of the characteristic function, where k_n is inductively given by k₀ = 0, k₁ = 1, and k_ℓ+1 = k_ℓ + 3^n-ℓ-1(4(k_ℓ + 1))^ℓDⁿ for 1 ≤ ℓ < n.