Download this article
 Download this article For screen
For printing
Recent Issues

Volume 28, 1 issue

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Moduli of spherical tori with one conical point

Alexandre Eremenko, Gabriele Mondello and Dmitri Panov

Geometry & Topology 27 (2023) 3619–3698
Abstract

We determine the topology of the moduli space 𝒮1,1(𝜗) of surfaces of genus one with a Riemannian metric of constant curvature 1 and one conical point of angle 2π𝜗. In particular, for 𝜗 (2m 1,2m + 1) nonodd, 𝒮1,1(𝜗) is connected, has orbifold Euler characteristic 1 12m2, and its topology depends on the integer m > 0 only. For 𝜗 = 2m + 1 odd, 𝒮1,1(𝜗) has 1 6m(m + 1) connected components. For 𝜗 = 2m even, 𝒮1,1(𝜗) has a natural complex structure and it is biholomorphic to 2Gm for a certain subgroup Gm of SL (2, ) of index m2, which is nonnormal for m > 1.

Keywords
spherical surfaces, moduli spaces, conical points, Belyi curves
Mathematical Subject Classification
Primary: 58D27
Secondary: 32Q20, 52B70
References
Publication
Received: 4 May 2021
Revised: 11 February 2022
Accepted: 9 April 2022
Published: 5 December 2023
Proposed: Benson Farb
Seconded: David M Fisher, Leonid Polterovich
Authors
Alexandre Eremenko
Department of Mathematics
Purdue University
West Lafayette, IN
United States
Gabriele Mondello
Dipartimento di Matematica Guido Castelnuovo
Sapienza Università of Roma
Roma
Italy
Dmitri Panov
Department of Mathematics
King’s College London
London
United Kingdom

Open Access made possible by participating institutions via Subscribe to Open.