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March 2021 Degenerating families with finite monodromy groups
Takayuki Okuda
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Kodai Math. J. 44(1): 1-19 (March 2021). DOI: 10.2996/kmj44101

Abstract

A degenerating family of Riemann surfaces over a Riemann surface gives us a monodromy representation, which is a homomorphism from the fundamental group of a punctured surface to the mapping class group. We show that, given such a homomorphism, if its image is finite, then there exists an (isotrivial) degenerating family of Riemann surfaces whose monodromy representation coincides with it. Moreover, we discuss the special sections of such a degenerating family.

Acknowledgment

The author would like to thank Shigeru Takamura for very fruitful discussion and warm encouragement. The author is partially supported by the Fujukai Foundation.

The author also thanks the anonymous referee for giving very useful comments on an earlier version of the paper.

Citation

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Takayuki Okuda. "Degenerating families with finite monodromy groups." Kodai Math. J. 44 (1) 1 - 19, March 2021. https://doi.org/10.2996/kmj44101

Information

Received: 9 October 2018; Revised: 21 October 2019; Published: March 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.2996/kmj44101

Subjects:
Primary: 14D06
Secondary: 14D05 , 14H15

Keywords: Degeneration of Riemann surfaces , Holomorphic fibration , mapping class group , Monodromy , Quotient family , quotient singularity

Rights: Copyright © 2021 Tokyo Institute of Technology, Department of Mathematics

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Vol.44 • No. 1 • March 2021
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