  Slowly divergent geodesics in the moduli space of Riemann surfaces of genus
at least 2 are constructed via cyclic branched covers of the torus. Nonergodic
examples (i.e. geodesics whose defining quadratic differential has nonergodic
vertical foliation) diverging to infinity at sublinear rates are constructed
using a Diophantine condition. Examples with an arbitrarily slow prescribed
growth rate are also exhibited.
