×

zbMATH — the first resource for mathematics

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)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abikoff, W., Degenerating families of Riemann surfaces, Ann. Math., 105, 1, 29-94 (1977) · Zbl 0347.32010
[2] Broughton, SL, The equisymmetric stratification of the moduli space and the Krull dimension of mapping class groups, Topol. Appl., 37, 101-113 (1990) · Zbl 0747.32017
[3] Díaz, R.; González-Aguilera, V., Limit points of the branch locus of \(\cal{M}_g\), Adv. Geom., 19, 4, 505-526 (2019) · Zbl 1435.32015
[4] Luo, F.; Stong, R., Dehn-Thurston coordinates for curves in surfaces, Commun. Anal. Geom., 12, 1, 1-41 (2004) · Zbl 1072.57012
[5] Miranda, R., Graph Curves and Curves on \(K3\) Surfaces. International Centre for Theoretical Physics, Trieste, 119-176 (1989), Singapore: World Scientific, Singapore · Zbl 0800.14014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.