Differential operators on monomial curves.
Let \(k\) be a fixed algebraically closed field of characteristic 0, and \(X\) an affine monomial curve defined over \(k\). Then, \(X = \text{Spec}(A)\), where \(A=k[\Gamma]\) is the semigroup algebra over \(k\) defined by a numerical semigroup \(\Gamma\subseteq {\mathbb N}_0\). The author gives an explicit description of the ring \(D={\roman D}(A)\) of \(k\)-linear differential operators on \(A\), the associated graded ring \(\text{GR}{\roman D}(A)\), and the module of derivations \(\text{Der}_k(A)\). He also classifies all graded \(D\)-modules which are finitely generated torsion-free \(A\)-modules of rank 1, considered as modules over the subring \(A\subseteq {\roman D}(A)\).
scientific article; zbMATH DE number 1955953