  We consider a generalized Riemann-Hurwitz formula as it may be applied to
rational maps between projective varieties having an indeterminacy set and
fold-like singularities. The case of a holomorphic branched covering map is
recalled. Then we see how the formula can be applied to iterated maps having
branch-like singularities. Separately, we consider a further application
involving the Chern classes of determinantal varieties when the latter are
realized as the degeneracy loci of certain vector bundle morphisms.
