  In this paper we investigate Abel maps on normal surface singularities
described in \cite{NNI}. We investigate the affine version of the class of the
images of Abel maps on normal surface singularities. More precisely we consider
the projective clousure of the image of an Abel map, its dual projective
variety and we substract from its degree the multiplicity of the infinite
hyperplane on the dual variety. In the case of generic singularities we prove
explicit combinatorial formulas of this invariant, in the general case we prove
an upper bound.
