  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 $\nabla: \operatorname{Der}_k(A) \to
\operatorname{End}_k(M)$ that satisfy the derivation property and preserves the
Lie product.
  In particular, a torsion free module N over the complete local ring $B = \hat
A$ admits a natural integrable connection if A is a simple curve singularity,
or if A is irreducible and N is a gradable module.
