GONALITY AND CLIFFORD INDEX OF PROJECTIVE CURVES ON RULED SURFACES

摘要

Let X be a smooth curve on a ruled surface π : S → C. In this paper, we deal with the questions on the gonality and the Clifford index of X and on the composedness of line bundles on X with the covering morphism π|_X. The main theorem shows that if a smooth curve X～aCo+bf satisfies some conditions on the degree of b, then a line bundle F on X with Cliff (F) ≤ ag(C) - 1 is composed with π|_X. This implies that a part of the gonality sequence of X is computed by the gonality sequence of C as follows: d_r(X)=ad_r(C) for r ≤ L. where L is the length of the gonality sequence of C.