 Riemann–Hurwitz formula

For a degree-$d$ holomorphic map, $2g_X-2=d(2g_Y-2)+\sum (e_p-1)$.

The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex geometry that relates the properties of a branched cover of Riemann surfaces (or algebraic curves) to the properties of its base surface and the branching behavior of the cover.