DIFFERENTIAL-OPERATORS, N-BRANCH CURVE SINGULARITIES AND THE N-SUBSPACE PROBLEM

Let R be the coordinate ring of a smooth affine curve over an algebrai cally closed field of characteristic zero k. For S a subalgebra of R w ith integral closure R denote by D(S) the ring of differential operato rs on S and by H(S) the finite-dimensional factor of D(S) by its uniqu e minimal ideal. The theory of diagonal n-subspace systems is introduc ed. This is used to show that if A is a finite-dimensional k-algebra a nd t greater than or equal to 1 is any integer there exists such an S with [GRAPHICS] Further, the Morita classes of H(S) are classified for curves with few branches, and it is shown how to lift Morita equivale nces from H(S) to D(S).