The base and the family. Let ∆ = ∆(3, 4, ∞) be the triangle group, acting on the upper half plane h; the quotient h/∆ is P1 minus a point, and adding the cusp gives P1 with orbifold points of orders 3 and 4 and the cusp. Let V ∼= Z4 carry automorphisms T1, T2 of orders 3 and 4 with T0 := (T1T2)−1 unipotent, (T0 − I)2 = 0: this is a representation ∆ → SL(V), and we let it act on the dual ...