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The Weierstrass semigroup of a pair of Galois Weierstrass points with prime degree on a curve. (English) Zbl 1082.14036

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)].

MSC:

14H55 Riemann surfaces; Weierstrass points; gap sequences
14H30 Coverings of curves, fundamental group
14H45 Special algebraic curves and curves of low genus
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