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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
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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

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