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Limits of equisymmetric $1$-complex dimensional families of Riemann surfaces

Antonio F. Costa, Víctor González-Aguilera


We describe the limit surfaces of some equisymmetric $1$-complex dimensional families of Riemann surfaces in the boundary of the Deligne-Mumford compactification of moduli space. We provide a description of such nodal Riemann surfaces in terms of the group of automorphisms defining the family. We apply our method to some known examples.

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