Elliptic pencil on a K3 surface
= Elliptic pencil on a K3 surface
{title2=$E^2=0,\quad |E|\cong\mathbb P^1$}
A primitive effective nef class of square zero on a complex <K3 surface> defines a basepoint-free pencil with connected genus-one fibres. Its general fibre is a smooth <elliptic curve>. A section is a <smooth rational curve> $\Gamma$ with $E\cdot\Gamma=1$ and $\Gamma^2=-2$.