Double Coverings of Non-orientable Riemann Surfaces Ramified over Discrete Sets

摘要

We find an upper bound for the number of non-equivalent twofold coverings of closed non-orientable surfaces with conformal structures, ramified over sets with isolated points, by a given surface of topological genus g ≥ 3 with such structure and we characterize configurations for which our bounds are attained. We split our study according to whether the covering surface is symmetric or not and whether the corresponding coverings are decomposable or not in a suitable sense.