= Canonical genus-four curve as a quadric-cubic intersection
{title2=$C=V(Q_2,F_3)\subseteq\mathbb P^3$}
For a nonhyperelliptic <smooth projective curve> of <geometric genus> four, the <canonical map> is an embedding of degree six. Dimension counts $10>h^0(2K)=9$ and $20>h^0(3K)=15$ supply a quadric and a cubic not divisible by it. The quadric is irreducible because the curve is nondegenerate. Degree six and <unmixedness of a complete intersection> then identify the intersection with the curve as a scheme.
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