Locus of curves with D_n-symmetry inside M_g

2015/08/18 by Binru Li, Li, Binru, Sascha Weigl +1
Mathematics · #14H10 #14H15 #14H30 #32G15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1508.04264

openalex publication_date 2015/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to determine the irreducible components of M_g(D_n), the locus inside M_g of the curves admitting an effective action by the dihedral group D_n. This is done by classifying pairs (H,H') of distinct subgroups of the mapping class group Map_g, such that both H and H' are isomorphic to D_n and the fixed point locus of H inside the Teichmüller space T_g is contained in the fixed point locus of H'.

Citations

• Irreducibility of Hurwitz spaces

Related

• Effective curves on M_0,n from group actions
• The irreducible components of the moduli space of dihedral covers of algebraic curves
• Hidden symmetries of the Grothendieck--Teichmüller group
• Curves with prescribed symmetry and associated representations of\n mapping class groups
• Computing discrete invariants of varieties in positive characteristic. I. Ekedahl-Oort types of curves