# zbMATH — the first resource for mathematics

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
##### Keywords:
Weierstrass semigroup
Full Text:
##### 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.