Solution
= Solution
For a nonconstant <holomorphic map> $f:X\to Y$ between compact connected <Riemann surfaces>, let $n$ be its degree and $e_p$ its local degree at $p$. The <Riemann-Hurwitz formula> is
$$
\boxed{\chi(X)=n\chi(Y)-\sum_{p\in X}(e_p-1).}
$$
Equivalently, $2g_X-2=n(2g_Y-2)+\sum_p(e_p-1)$. Only finitely many terms are nonzero; their sum is the total ramification. In local coordinates the map has the form $w=z^{e_p}$ after suitable coordinate changes.