Uniformization of surfaces of genus two with automorphisms (Q1114778)

Let C be a Riemann surface of genus two admitting an involution besides the hyperelliptic one (which is denoted by i), and consider the tori obtained as quotients of C by \(<\sigma >\) and by \(<i\sigma >\). The authors completely describe the relations occurring among the non euclidean polygons uniformizing C, the Riemann matrix of C and the equations of the tori above. When C is described as a quartic with a double point, some geometrical property of bitangents of C is proven. Finally, for each possible group automorphisms of C the corresponding polygon is characterized.