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On monodromies of holomorphic families of Riemann surfaces and modular transformations

  • HIROSHIGE SHIGA (a1)
    • Published online: 01 November 1997
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.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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