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On the index of the Weierstrass semigroup of a pair of points on a curve. (English) Zbl 0815.14020
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.

MSC:
14H55 Riemann surfaces; Weierstrass points; gap sequences
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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
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