Narrow Results

In this work, we prove that the hyperelliptic branch locus of orientable Klein surfaces of genus $g$ with one boundary component is connected and in the case of non-orientable Klein surfaces it has $\frac{g+1}{2}$ components, if $g$ is odd, and $\frac{g+2}{2}$ components for even $g$. We notice that, for non-orientable Klein surfaces with two boundary components, the hyperelliptic branch loci are connected for all genera.