Let $F:X\rightarrow Y$ be a non constant holomorphic map between compact Riemann surfaces, Then
$2g(X)-2=deg(F)(2g(Y)-2)+\sum_{p\in X}[mult_p(F)-1]$.
I am studying the proof from Rick Miranda's Algebraic curves and Riemann surfaces.
Proof: Take a triangulation of $Y$ , such that each branch point of $F$ is the vertex . Assume that there are $v$ vertices , $e$ edges and $t$ triangles. Lift this triangulation to $X$ via the map $F$.
Here is my question. If there is no branch point what will happen ?