= Semistable infinite chain from a toric fan
{title2=$U_i=\operatorname{Spec}\mathbb Z[x_i,y_i],\quad q=x_i y_i$}
Take rays $(i,1)$ and cones generated by consecutive rays in $\mathbb Z^2$. Their dual generators $(1,-i)$ and $(-1,i+1)$ give $x_i=tq^{-i}$, $y_i=t^{-1}q^{i+1}$. Adjacent charts glue by $x_{i+1}=y_i^{-1}$, $y_{i+1}=x_i y_i^2$. The fibre $q=0$ is a chain of <projective lines>: each component has two affine-line charts joined by reciprocal coordinates, and consecutive components meet at one node. Inverting $q$ identifies all charts with the <multiplicative group scheme> over $\mathbb Z[q,q^{-1}]$. The local node algebra is free over $\mathbb Z[q]$, with <basis> $1,x_i^a,y_i^b$ for $a,b\geq1$, so the morphism is flat.
// Target: toric-geometry.bigb
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