The Moduli of Klein Covers of Curves

Abstract

We study the moduli space $V_4{\mathcal{M}}_g$ of Klein four covers of genus $g$ curves and its natural compactification. This requires the construction of a related space which has a choice of basis for the Klein four group. This space has the interesting property that the two components intersect along a component of the boundary. Further, we carry out a detailed analysis of the boundary, determining components, degrees of the components over their images in $\overline{{\mathcal{M}}_g}$, and computing the canonical divisor of $\overline{V_4{\mathcal{M}}_g}$.

18 pages