The Weierstrass points of bielliptic curves (Q1279775)

Let \(E\) be a complex elliptic curve and \(\pi:X \rightarrow E\) a double cover with \(g\), the genus of \(X\), at least 6. Then \(X\) is bielliptic. The authors list the possible non-gap-sequences for Weierstrass points. They use that the canonical model \(Y \subset \mathbb{P}^{g-1}\) of \(X\) is contained in a cone \(T\). This cone has as base a linearly normal degree \(g-1\) elliptic curve \(C\) which is naturally isomorphic to \(E\). A careful study of the ramification of \(T\) intersected with a hyperplane over \(C\) eventually yields the desired result.