Generating Vector (reviewed)

The generating vector of a group of automorphisms $G$ acting on a compact Riemann surface $X$ is a list of generators for the monodromy group of $G$ obtained by taking the image of the standard generators for $\pi_1(Y-B,y_0)$ under the image of the map $\rho\colon \pi_1(Y-B,y_0)\to S_d$ used to define the monodromy group, where $B$ is the set of branch points of the projection $\phi\colon X\to Y=X/G$, and $y_0$ is any point on $Y$ that is not in $B$.