The Weierstrass semigroup of a pair of Galois Weierstrass points with prime degree on a curve
A Galois Weierstrass point with degree \(n\) means a total ramification point of a cyclic covering of the projective line of degree \(n\). In this paper the authors describe the Weierstrass semigroup of a Galois Weierstrass point with prime degree using Morrison-Pinkham equalities [\textit{I. Morrison} and \textit{H. Pinkham}, Ann. Math. (2) 124, 591--625 (1986; Zbl 0624.14018)]. Then they give a condition on the Weierstrass semigroups for existence of a pair of Galois Weierstrass points with prime degree by constructing the defining equation of the curve using their result in \textit{S. J. Kim} and \textit{J. Komeda} [Arch. Math. 76, 265--273 (2001; Zbl 1076.14518)].
Weierstrass semigroup of a pair of points
scientific article; zbMATH DE number 2176480