l-away ACM bundles on Fano surfaces

We propose the definition of l-away ACM bundle on a polarized variety (X,O-X(h)). Then we give constructions of l-away ACM bundles on (P-2,O-P2(1)), (P(1)xP(1),O-P(xP)1(1)(1,1)) and the anticanonically polarized blow up of P-2 up to three non collinear points. Also, we give the complete classification of l-away ACM bundles E of rank 2 for values 1 <= l <= 2 on (P-2,O-P2(1)). Similarly, on (P(1)xP(1),O-P1xP1(1,1)), we give such a classification if det(E)=O-P1xP1(a,a) for some a is an element of Z. Moreover, we prove that the corresponding graded module H-*(1) (epsilon) = circle plus H-t is an element of Z(1)(epsilon(th)) is connected, extending the similar result for bundles on P-2.