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.
Kodai Math. J.
44(1):
1-19
(March 2021).
DOI: 10.2996/kmj44101
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