NON-CYCLIC WEIERSTRASS SEMIGROUPS

摘要

Morrison and Pinkham [5] gave a characterization of the semigroups of Galois Weierstrass points, i.e., total ramification points of cyclic coverings of the projective line of degree n. They showed that such a semigroup must satisfy certain equalities, which we call the M-P equalities in this paper, and that the converse holds for any prime n = p ≤ 7. In this paper we consider the case when n = p is a prime number ≥ 11. In the case p = 11 we investigate whether a primitive numerical semigroup satisfying the M-P equalities is the semigroup of a Galois Weierstrass point. For each prime p ≥ 13, we give a Weierstrass semigroup which satisfies the M-P equalities but is not the semigroup of a Galois Weierstrass point. For these, we study the semigroups of Galois Weierstrass points using the equations defining curves which are cyclic covering of the projective line of degree p.