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 $2$.
How to prove that any genus 2 curve is hyperelliptic?
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algebraic-geometry
complex-geometry
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0$|K_X|=\mathbb{P}^1$ and the canonical map gives the double cover. I made a mistake in my old computation. Thanks. – 2012-12-03