NUMBER OF WEAK GALOIS-WEIERSTRASS POINTS WITH WEIERSTRASS SEMIGROUPS GENERATED BY TWO ELEMENTS

Abstract

Let C be a nonsingular projective curve of genus ≥ 2 over an algebraically closed field of characteristic 0. For a point P in C, the Weierstrass semigroup H(P ) is defined as the set of non-negative integers n for which there exists a rational function f on C such that the order of the pole of f at P is equal to n, and f is regular away from P . A point P in C is referred to as a weak Galois-Weierstrass point if P is a Weierstrass point and there exists a Galois morphism φ : C → P1 such that P is a total ramification point of φ. In this paper, we investigate the number of weak Galois-Weierstrass points of which the Weierstrass semigroups are generated by two positive integers.