  Inspired by a result of D. Cerveau on surjective derivations on a polynomial
ring in two variables over a complex number field C, we consider a surjective
derivation defined on an affine domain over C of dimension one or two. Though
our proofs are mostly algebraic or algebro-geometric, the idea using a result
of Dimca-Saito which is behind the arguments of Cerveau and based on the
differential complex of the polynomial ring in n variables is inspiring and
affects our arguments.
