Existence of nonarithmetic monodromy groups - Mostow, G. D. (1981)
In an 1885 paper, E. Picard defined a subgroup Τ(Λ) of PU(2,1) generated by monodromies and depending on parameters Λ = (λ(1),λ(2),λ(3),λ(4)), 0 < λ(i) < 1, < λ(i) < 3, λ(i) + λ(j) ≥ 1, 1 ≤ i < j ≤ 4. The family Τ(Λ) resembles the family of groups Τ([unk]) defined in 1978 but is a different family. In common with the groups Τ([unk]), (i) Τ(Λ) is discrete for a finite number of Λ, (ii) Τ(Λ) is a nonarithmetic lattice for some Λ, and (iii) for all Λ ∈ [unk](4), there is a compact complex surface S(Λ) with π(1) [S(Λ)] of finite index in Τ(Λ).