Kim, Seon Jeong; Komeda, Jiryo The Weierstrass semigroup of a pair of Galois Weierstrass points with prime degree on a curve. (English) Zbl 1082.14036 Bull. Braz. Math. Soc. (N.S.) 36, No. 1, 127-142 (2005). 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 [I. Morrison and 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 S. J. Kim and J. Komeda [Arch. Math. 76, 265–273 (2001; Zbl 1076.14518)]. Reviewer: Ryutaro Horiuchi (Kyoto) Cited in 2 Documents MSC: 14H55 Riemann surfaces; Weierstrass points; gap sequences 14H30 Coverings of curves, fundamental group 14H45 Special algebraic curves and curves of low genus Keywords:Weierstrass semigroup of a point; Weierstrass semigroup of a pair of points Citations:Zbl 0624.14018; Zbl 1076.14518 PDFBibTeX XMLCite \textit{S. J. Kim} and \textit{J. Komeda}, Bull. Braz. Math. Soc. (N.S.) 36, No. 1, 127--142 (2005; Zbl 1082.14036) Full Text: DOI