  Let M be a Q-divisor on a smooth surface over C. In this paper we give
criteria for very ampleness of the adjoint of the round-up of M. (Similar
results for global generation were given by Ein and Lazarsfeld and used in
their proof of Fujita's Conjecture in dimension 3.) In the last section we
discuss an example which suggests that this kind of criteria might also be
useful in the study of linear systems on surfaces.
