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

Abstract.

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 $n\leqq 7$. 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.