The Moduli of Klein Covers of Curves

2014/07/14 by Charles Siegel, Siegel, Charles
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1407.3530

Abstract

We study the moduli space V₄M_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 M_g, and computing the canonical divisor of V₄M_g.

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