Adjoint linear systems on normal surfaces

We prove that to check whether the adjoint line bundle K-X + L (with L nef and L-2 sufficiently large) on a normal projective surface X is spanned (ve ry ample) it is necessary and sufficient to check it on curves of low degre e and bounded genus (this is a generalisation of Reider's theorem). its an application we deduce a more precise version of this criterion for surfaces with only Du Val singularities and prove a conjecture of F. Catanese, M. F ranciosi, K. Hulek, and M. Reid on bicanonical maps of canonical surfaces.