Cyclic covers of Stable curves and their moduli spaces

Abstract

We study the deformation of $G$-marked stable curves in the case where $G$ is a cyclic group, and construct a parameterizing space for $G$-marked stable curves of a given numerical type. This is then used in order to study the components of the locus of stable curves admitting the action of a cyclic group of non prime order $d$, extending work of F. Catanese in the case where $d$ is prime.

14 pages

References in corpus (2)

• Genus stabilization for moduli of curves with symmetries
• Locus of curves with D_n-symmetry inside M_g