Branched covering

Summary

A branched covering is a map that is a covering map except over a discrete set of branch values, where several sheets come together. For Riemann surfaces, every non-constant proper holomorphic map is a branched covering of finite degree. Branched coverings of the Riemann sphere describe compact Riemann surfaces as the surfaces of multivalued algebraic functions, and the Riemann–Hurwitz formula computes their genus.