Abstract.
Let C g,n be a compact surface of genus g having n punctures, T g,n the associated Teichmüller space, and Γ g,n the corresponding Teichmüller modular group. We will show that for any subgroup Γ≤Γ g,n , Γ T g,n ≔ T g,n /Γ is a moduli space of curves having Γ-structure. Furthermore, we will investigate for which Γ≤Γ g,n and for which finite coverings P : C g′,n′ →C g,n there exists a holomorphic map Φ P : Γ T g,n → Γ′T g′,n′ such that for any R ? Γ T g,n , Φ P (R) → R is topologically equivalent to P.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 14 May 2001 / Revised version: 2 November 2001
Rights and permissions
About this article
Cite this article
Mayer, J. Morphisms between the moduli spaces of curves with generalized Teichmüller structure. Manuscripta Math. 107, 229–249 (2002). https://doi.org/10.1007/s002290100236
Issue Date:
DOI: https://doi.org/10.1007/s002290100236