Gonality of a smooth plane quartic
= Gonality of a smooth plane quartic
{title2=$\operatorname{gon}(C)=3$}
Projection from a point of a <smooth plane quartic> gives a degree-three map to the <projective line>. A degree-two map would make the curve <hyperelliptic curve>[hyperelliptic], but its <canonical map of a smooth plane curve>[canonical map] is its plane embedding, whereas a hyperelliptic canonical map is not an embedding. Its <gonality> is therefore three.