Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T13:23:47.282Z Has data issue: false hasContentIssue false
  • English
  • Français

On monodromies of holomorphic families of Riemann surfaces and modular transformations

Published online by Cambridge University Press:  01 November 1997

HIROSHIGE SHIGA
HIROSHIGE SHIGA
Affiliation:
Department of Mathematics, Tokyo Institute Technology, Oh-okayama, Meguro-ku, Tokyo, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

A locally non-trivial holomorphic family of Riemann surfaces over a hyperbolic Riemann surface B determines a homomorphism (monodromy) of the fundamental group of B to the modular group. We give a necessary condition for a homomorphism to be a mondromy of a holomorphic family of Riemann surfaces. And we estimate the number of holomorphic families in terms of topological information for holomorphic families over Riemann surfaces of genus 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 3 , November 1997 , pp. 541 - 549
Copyright
Cambridge Philosophical 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.)