Hyperelliptic linear system on a K3 surface
= Hyperelliptic linear system on a K3 surface
{title2=$\deg\varphi_{|D|}=2$}
= Hyperelliptic linear systems on a K3 surface
{synonym}
For a basepoint-free nef big divisor $D$, this means that the morphism given by its complete system is generically two-to-one onto its image. Equivalently, its general smooth curve is <hyperelliptic>. A double cover of $\mathbb P^2$ branched over a smooth sextic, with the pullback of $\mathcal O(1)$, gives the degree-two example.