Kodai Mathematical Journal

A remark on universal coverings of holomorphic families of Riemann surfaces

Yoichi Imayoshi and Minori Nishimura

Full-text: Open access

Abstract

We study the universal covering space $\tilde M$ of a holomorphic family (M, π, R) of Riemann surfaces over a Riemann surface R. The main result is that (1) $\tilde M$ is topologically equivalent to a two-dimensional cell, (2) $\tilde M$ is analytically equivalent to a bounded domain in C2, (3) $\tilde M$ is not analytically equivalent to the two-dimensional unit ball B2 under a certain condition, and (4) $\tilde M$ is analytically equivalent to the two-dimensional polydisc Δ2 if and only if the homotopic monodoromy group of (M, π, R) is finite.

Article information

Source
Kodai Math. J., Volume 28, Number 2 (2005), 230-247.

Dates
First available in Project Euclid: 11 August 2005

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1123767005

Digital Object Identifier
doi:10.2996/kmj/1123767005

Mathematical Reviews number (MathSciNet)
MR2153912

Zentralblatt MATH identifier
1082.30032

Citation

Imayoshi, Yoichi; Nishimura, Minori. A remark on universal coverings of holomorphic families of Riemann surfaces. Kodai Math. J. 28 (2005), no. 2, 230--247. doi:10.2996/kmj/1123767005. https://projecteuclid.org/euclid.kmj/1123767005


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