Automorphismen und Modulraum Galoisscher dreiblättriger Überlagerungen (Q1063151)

Let \(M_ g\) denote the space of isomorphism classes of compact Riemann surfaces of genus g. Consider the subset \(M^ 3_ g\) of \(M_ g\) which consists of those Riemann surfaces that admit a threefold Galois cover over \({\mathbb{P}}^ 1\). In this work the space \(M^ 3_ g\) is parametrized using branch points of the Galois covers. It turns out that \(M^ 3_ 3\) is connected but for \(g>3\) \(M^ 3_ g\) is not connected. The authors give a formula for the number of components of a general \(M^ 3_ g\) and give rather explicit descriptions of them as well. The paper ends with a list of the automorphism groups of certain threefold Galois covers of \({\mathbb{P}}^ 1\) of genus g for \(g=3,4,5,6\).