Ramification points of double coverings of curves and Weierstrass points (Q1570438)

Let \(\pi: X \rightarrow C\) be a double covering with \(X\) a smooth curve and \(C\) an elliptic curve. It is known that every point in the ramification locus of \(\pi\) is a Weierstrass point of \(X\). In this paper the authors study not just the gap sequence of a single Weierstrass point of \(X\) [see \textit{J. Park}, Manuscr. Math. 95, 33-45 (1998; Zbl 0915.14020)], but the gap sequence of all points of the ramification locus of \(\pi\). In particular, following \textit{E. Ballico} and \textit{S. J. Kim} [Indag. Math., New Ser. 9, No. 2, 155-159 (1998; Zbl 0930.14023)], they prove the existence of bielliptic curves with a certain number of suitable ramification Weierstrass points and a non-ramification Weierstrass point with prescribed sequence of non-gaps. They also study the problem for triple cyclic coverings of elliptic curves.