  For each positive integer $t$ and each sufficiently large integer $r$, we
show that the maximum number of elements of a simple, rank-$r$, $\mathbb
C$-representable matroid with no $U_{2,t+3}$-minor is $t{r\choose 2}+r$. We
derive this as a consequence of a much more general result concerning matroids
on group-labeled graphs.
