Signature of a group action on a curve (reviewed)

Let $G$ be a group of automorphisms acting on a curve $X/\C$ of genus at least $2$, let $g_0$ be the genus of the quotient $Y:=X/G$, let $B$ be the set of branch points of the projection $\phi\colon X\to Y$, and let $m_1 \leq m_2 \leq \ldots \leq m_r$ be the orders of the standard generators for $\pi_1(Y-B,y_0)$ corresponding to the elements of $B=\{y_1,\ldots,y_r\}$.

The sequence of integers $[g_0; m_1, \ldots, m_r]$ is the signature of the group action.