On groups of automorphisms of compact Riemann surfaces of genus four (Q1090442)

The authors present a complete classification of the possible groups of automorphisms of closed Riemann surfaces of genus four defined by an equation of the form \(w^ 3-w=P_ 5(z)\) (a polynomial for degree 5.) Beside the trivial group, which occurs generalically, the possibilities are \({\mathbb{Z}}_ 2\), \({\mathbb{Z}}_ 5\) and \({\mathbb{Z}}_{10}\). The associated generators, and the moduli spaces are given explicitly. In a future paper the case of hyperelliptic surfaces of genus four will be treated completely.