Genus-two Weierstrass gap sequence
= Genus-two Weierstrass gap sequence
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On a genus-two smooth projective curve, the gap set at any point is either $\{1,2\}$ or $\{1,3\}$. The integer $1$ is always a gap on a positive-genus curve. If $2$ is not a gap, then $3$ must be a gap, since pole orders are closed under addition and $2,3$ would otherwise generate every integer at least two.