I want to show the following:
Let $F:X\rightarrow Y$ be a non-constant and holomorphic map between compact riemann surfaces with $genus(X)=genus(Y)\geq 2$.
In the above it holds that $F$ is an isomorphism.
I am pretty sure that I should use the formula of riemann-hurwitz which can be found here. But I wasnt able to proof the statement.
Hopefully someone can help me.