Cyclic covers of Stable curves and their moduli spaces
Binru Li

TL;DR
This paper investigates the deformation theory of cyclic group actions on stable curves and constructs a parameter space for such curves, extending previous work to non-prime order cyclic groups.
Contribution
It introduces a new parameter space for G-marked stable curves with cyclic groups of non-prime order, expanding the understanding of their moduli.
Findings
Constructed a parameter space for G-marked stable curves of given type
Extended Catanese's work to cyclic groups of non-prime order
Analyzed components of the locus of stable curves with cyclic automorphisms
Abstract
We study the deformation of -marked stable curves in the case where is a cyclic group, and construct a parameterizing space for -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 , extending work of F. Catanese in the case where is prime.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows · Geometry and complex manifolds
