Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T13:48:21.054Z Has data issue: false hasContentIssue false
  • English
  • Français

CONFORMAL VERSUS TOPOLOGICAL CONJUGACY OF AUTOMORPHISMS ON COMPACT RIEMANN SURFACES

Published online by Cambridge University Press:  01 May 1997

GABINO GONZÁLEZ-DIEZ  and
RUBÉN A. HIDALGO
GABINO GONZÁLEZ-DIEZ
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
RUBÉN A. HIDALGO
Affiliation:
Departamento de Matemáticas, Universidad Técnica Federico, Santa María Casilla 110-V, Valparaiso, Chile
Get access

Abstract

We produce a family of algebraic curves (closed Riemann surfaces) Sλ admitting two cyclic groups H1 and H2 of conformal automorphisms, which are topologically (but not conformally) conjugate and such that S/Hi is the Riemann sphere [Copf ]ˆ. The relevance of this example is that it shows that the subvarieties of moduli space consisting of points parametrizing curves which occur as cyclic coverings (of a fixed topological type) of [Copf ]ˆ need not be normal.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 3 , May 1997 , pp. 280 - 284
Copyright
© The London Mathematical Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)