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 L_st∈C(t)[d/dt] is constructed. For n=2 this is essentially Klein's work. For n>2 an actual calculation of L_st is done by computing an evaluation of invariants C[X₁,…,X_n]^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.