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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 \(\mathcal{P}_n\).

32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
14H10 Families, moduli of curves (algebraic)
Full Text: DOI
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