A note on Weierstrass points of bielliptic curves
A bielliptic curve \(X\) is a two sheeted cover \(\pi:X \rightarrow E\) of an elliptic curve \(E\). The author investigates such curves for genus \(g \geq 6\). Using results of \textit{J. Komeda} [J. Reine Angew. Math. 341, 68-86 (1983; Zbl 0498.30053)], the author characterizes the \(2g-2\) ramification points of \(\pi\) as Weierstrass points with only two possible non gap sequences (H) and (L). In the main result he shows that for any preassigned number \(s\), \(0 \leq s\leq 2g-2\), \(s \neq 2\), \(2g-3\), a bielliptic curve \(X\) with \(s\) Weierstrass points of type (H) and \(2g-2-s\) points of type (L) exists.
scientific article; zbMATH DE number 1135223