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How can one prove that any genus $2$ smooth curve is hyperelliptic? Remember that a smooth curve $C$ is called hyperelliptic if there exists a morphism $\phi:C \rightarrow \mathbb{P}^1$ of degree $2$.

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Hint: Consider the map by the linear system $|K_C|$. – Matt Dec 3 '12 at 0:01
$|K_X|=\mathbb{P}^1$ and the canonical map gives the double cover. I made a mistake in my old computation. Thanks. – M. K. Dec 3 '12 at 4:39

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