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July, 2017 Degenerations and fibrations of Riemann surfaces associated with regular polyhedra and soccer ball
Ryota HIRAKAWA, Shigeru TAKAMURA
J. Math. Soc. Japan 69(3): 1213-1233 (July, 2017). DOI: 10.2969/jmsj/06931213

Abstract

To each of regular polyhedra and a soccer ball, we associate degenerating families (degenerations) of Riemann surfaces. More specifically: To each orientation-preserving automorphism of a regular polyhedron (and also of a soccer ball), we associate a degenerating family of Riemann surfaces whose topological monodromy is the automorphism. The complete classification of such degenerating families is given. Besides, we determine the Euler numbers of their total spaces. Furthermore, we affirmatively solve the compactification problem raised by Mutsuo Oka — we explicitly construct compact fibrations of Riemann surfaces that compactify the above degenerating families. Their singular fibers and Euler numbers are also determined.

Citation

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Ryota HIRAKAWA. Shigeru TAKAMURA. "Degenerations and fibrations of Riemann surfaces associated with regular polyhedra and soccer ball." J. Math. Soc. Japan 69 (3) 1213 - 1233, July, 2017. https://doi.org/10.2969/jmsj/06931213

Information

Published: July, 2017
First available in Project Euclid: 12 July 2017

zbMATH: 06786995
MathSciNet: MR3685042
Digital Object Identifier: 10.2969/jmsj/06931213

Subjects:
Primary: 14D06
Secondary: 57M99, 58D19

Rights: Copyright © 2017 Mathematical Society of Japan

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Vol.69 • No. 3 • July, 2017
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