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Boundary of the pyramidal equisymmetric locus of $$\mathcal{M}_n$$. (English) Zbl 07260773
Summary: The augmented moduli space $$\widehat{\mathcal M}_n$$ is a compactification of moduli space $$\mathcal M_n$$ obtained by adding stable hyperbolic surfaces. The different topological types of the added stable surfaces produce a stratification of $$\partial \widehat{\mathcal M}_n$$. Let $$\mathcal{P}_n \subset \mathcal{M}_n$$ be the pyramidal locus in moduli space, i.e., the set of hyperbolic surfaces of genus $$n$$ such that the topological action of its preserving-orientation isometry group is the pyramidal action of the dihedral group $$D_n$$. The purpose of this paper is to state the complete list of strata in the boundary of $$\mathcal{P}_n$$.

##### MSC:
 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) 14H10 Families, moduli of curves (algebraic)
##### Keywords:
augmented moduli space; hyperbolic surfaces
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##### References:
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