= Nonaffine special fibre obtained by blowing up
Blow up $(0,1,0)$ in $\mathbb A^3_{x,y,z}$ and compose with $xy:\mathbb A^3\to\mathbb A^1$. Nonzero fibres are $\mathbb G_m\times\mathbb A^1$. The zero fibre consists of the strict transforms of the two coordinate planes and the exceptional $\mathbb P^2$, all with multiplicity one. Its plane crossings make it singular; its closed $\mathbb P^2$ makes it nonaffine. The centre is deliberately on just one component of $xy=0$, keeping the fibre reduced.
Back to article page
