Numerical semigroups which cannot be realized as semigroups of Galois Weierstrass points

摘要

Morrison and Pinkham [4] 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 $nleqq 7$ . In this paper we consider the case when n is a prime number $p geqq 11$ . For each prime $p geqq 11$ , we give a semigroup which satisfies the M-P equalities but is not the semigroup of a Galois Weierstrass point. For this, we study the semigroups of Galois Weierstrass points using the equations defining curves which are cyclic covering of the projective line.