On the classification of non-aCM curves on quintic surfaces in P³

In this paper, a curve is any projective scheme of pure dimension one. It is well known that the arithmetic genus and the degree of an aCM curve D in P-3 are computed by the h-vector of D. However, for a given curve D in P-3, the two aforementioned invariants of D do not tell us whether D is aCM or not. If D is an aCM curve on a smooth surface X in P-3, any member of the linear system | D+ lC| is also aCM for each non-negative integer l, where C is a hyperplane section of X. By a previous work, if a non-zero effective divisor D of degree d and arithmetic genus g on a smooth quintic surface X in P-3 is aCM and satisfies the condition h(0)(O-X ( D- C)) = 0, then 0 <= d+ 1- g <= 4. In this paper, we classify non-aCM effective divisors on smooth quintic surfaces in P-3 of degree d and arithmetic genus g such that 0 <= d + 1 - g <= 4, and give several examples of them.