A Riemann-Hurwitz-Plücker formula

We prove a simultaneous generalization of the classical Riemann-Hurwitz and Plücker formulas, addressing total number inflection points morphism from (smooth, projective) curve to an arbitrary higher-dimensional variety. Our definition point is relative algebraic family divisors on target variety, our formula obtained using theory localized top Chern classes. In assigning multiplicities points, we frequently have consider excess degeneracy loci, but are able show nonetheless that always nonnegative, positive under very mild hypotheses.