Ebene algebraische Kurven vom Typ p,q

Abstract

Let p,q be relatively prime integers with 2≤p<q. For r∈{1,...,p-1} let H ^p,q_r be the numerical semigroup generated by p,q,{(p−1) (q−1)−1−(ip+jq)¦i+j≤r−2}. Then there exists a smooth projective curve X and a point x on X, such that H ^p,q_r is the set of orders of poles of the rational functions on X, which are regular on X\{x}; in other words: H ^p,q_r is a Weierstraß semigroup.