Exercise 111.61.3. Let $k$ be an algebraically closed field. Let $X \subset \mathbf{P}^3_ k$ be a smooth curve of degree $d$ and genus $\geq 2$. Assume $X$ is not contained in a plane and that there is a line $\ell $ in $\mathbf{P}^3_ k$ meeting $X$ in $d - 2$ points. Show that $X$ is hyperelliptic.

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