On the index of the Weierstrass semigroup of a pair of points on a curve (Q1842020)

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.