Kim, Seon Jeong On the index of the Weierstrass semigroup of a pair of points on a curve. (English) Zbl 0815.14020 Arch. Math. 62, No. 1, 73-82 (1994). The author obtains exact formulas for the cardinality of the complement \(G(p,q)\) of the Weierstrass semigroup of a pair \((p,q)\) of points on a nonsingular complex projective curve \(C\). Using these formulas he obtains lower bounds and upper bounds on the cardinalities of such sets: \[ {g + 2 \choose 2} - 1 \leq \text{card} G(p,q) \leq {g + 2 \choose 2} - 1 - g - g^ 2. \] Moreover, considering examples, he shows that these bounds are sharp. Reviewer: Seon Jeong Kim (Chinju) Cited in 13 ReviewsCited in 38 Documents MSC: 14H55 Riemann surfaces; Weierstrass points; gap sequences Keywords:Weierstrass semigroup PDF BibTeX XML Cite \textit{S. J. Kim}, Arch. Math. 62, No. 1, 73--82 (1994; Zbl 0815.14020) Full Text: DOI References: [1] E.Arbarello, M.Cornalba, P.Griffiths, and J.Harris, Geometry of Algebraic Curves I. Berlin-Heidelberg-New York 1985. · Zbl 0559.14017 [2] R. J.Walker, Algebraic Curves, Princeton 1950. · Zbl 0039.37701 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.