具有有限单调群的退化族

IF 0.4 4区数学 Q4 MATHEMATICS

Kodai Mathematical Journal Pub Date : 2021-03-01 DOI:10.2996/KMJ44101

T. Okuda

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引用次数: 0

摘要

黎曼曲面上的退化黎曼曲面族给出了一个单态表示，即从穿孔曲面的基群到映射类群的同态。我们证明，给定这样一个同态，如果它的像是有限的，那么存在一个(等平凡的)退化黎曼曲面族，其单调表示与它一致。此外，我们还讨论了这样一个退化家庭的特殊部分。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Degenerating families with finite monodromy groups

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.

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来源期刊

Kodai Mathematical Journal 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Kodai Mathematical Journal is edited by the Department of Mathematics, Tokyo Institute of Technology. The journal was issued from 1949 until 1977 as Kodai Mathematical Seminar Reports, and was renewed in 1978 under the present name. The journal is published three times yearly and includes original papers in mathematics.