Global degenerating families with periodic monodromies (Theory of singularities of smooth mappings and around it)

Abstract

We prove that, given N powers of one surface periodic mapping class, if their composition coincides with the identity, then there exists a degenerating family of Riemann surfaces over a Riemann surface of arbitrary genus k with N singular fibers whose local monodromies correspond to the given N mapping classes respectively. We also show that, in the case (N, k) = (2, 0), the degenerating family constructed by our method has n (-1)-sections if the given mapping classes have n fixed points.