Trigonal linear system on a K3 surface
= Trigonal linear system on a K3 surface
{title2=$D\cdot E=3$}
= Trigonal linear systems on a K3 surface
{synonym}
For a basepoint-free nonhyperelliptic nef big divisor $D$, the trigonal condition means that its general smooth curve is a <trigonal curve>. An <elliptic pencil on a K3 surface> with $D\cdot E=3$ restricts to its degree-three pencil. On a smooth quartic containing a line $\Gamma$, the hyperplane class $H$ has this property for $E=H-\Gamma$.