Triangulations and moduli spaces of Riemann surfaces with group actions
type: Item
instance of: scholarly article
title: Triangulations and moduli spaces of Riemann surfaces with group actions
zbMATH Open document ID: 0854.30033
DOI: 10.1007/BF02567818
author: Peter Buser
author: R. Silhol
author: Mika Seppälä
published in: Manuscripta Mathematica
publication date: 1996-04-16T00:00:00Z
full work available at URL: https://eudml.org/doc/156123
review text: Let \(\overline {M^g}\) be the moduli space of stable compact genus \(g\) Riemann surfaces \((g \geq 2)\). This space may be thought of as the Baily-Mumford compactification of the moduli space \(M^g\) of compact smooth Riemann surfaces of genus \(g\). The authors give a new approach to this compactification which allows a generalization to the case of Riemann surfaces with group actions. First they explain their new approach by giving a new proof of the Mahler compactness theorem. The main result of the work under review is Theorem 2: For any finite group \(F\), the set \(\overline {M^g_F} : = \{[X] \in \overline {M^g} : F\) is isomorphic to a subgroup of \(\text{Isom} (X)\}\) is a compact subset of \(\overline M^g\). -- However, for general finite groups \(F\) the sets \(\overline {M^g_F}\) need not be connected. However, for \(\mathbb{Z}_2\)-actions, the above subset is connected. These results are based on new coordinates for moduli spaces which are obtained by certain regular triangulations of Riemann surfaces. The authors announce that these triangulations play also an important role in approximating eigenfunctions of the Laplacian.
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 14H15
zbMATH DE Number: 866163
zbMATH Keywords: moduli space
zbMATH Keywords: triangulations
reviewed by: Jürgen Elstrodt
MaRDI profile type: Publication
Wikidata QID: Q124840618
OpenAlex ID: W2030260312
description: scientific article; zbMATH DE number 866163