Linear differential equations with finite differential Galois group

For a finite irreducible subgroup H⊂PSL(Cn) and an irreducible, H-invariant curve Z⊂P(Cn) such that C(Z)H=C(t), a standard differential operator Lst∈C(t)[d/dt] is constructed. For n=2 this is essentially Klein's work. For n>2 an actual calculation of Lst is done by computing an evaluation of invariants C[X1,…,Xn]H→C(t) and applying a scalar form of a theorem of E. Compoint in a “Procedure”. Also in some cases where Z is unknown evaluations are produced. This new method is tested for n=2 and for three irreducible subgroups of SL3. This supplements [18]. The theory developed here relates to and continues classical work of H.A. Schwarz, G. Fano, F. Klein and A. Hurwitz.