Connections on modules over quasi-homogeneous plane curves

Let k be an algebraically closed field of characteristic 0, and let A=k[x, y]/(f) be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M, there exists a natural graded integrable connection, i.e., a graded A-linear homomorphism : Der(k)(A) --> End(k)(M), that satisfies the derivation property and preserves the Lie product. In particular, a torsion free module N over the complete local ring B = (A) over cap admits a natural integrable connection if A is a simple curve singularity, or if A is irreducible and N is a gradable module.