# Riemann-Hurwitz formula

From Citizendium

In algebraic geometry the **Riemann-Hurwitz formula**, named after Bernhard Riemann and Adolf Hurwitz, states that if *C*, *D* are smooth algebraic curves, and is a finite map of degree *d* then the number of branch points of *f*, denoted by *B*, is given by

*D*such that all the branch points of the map are nodes of the triangulation. One then considers the pullback of the triangulation to the curve

*C*and computes the Euler characteristics of both curves.