  We prove there exist solutions to the focusing cubic nonlinear Schr\"odinger
equation in three dimensions that blowup on a circle, in the sense of L^2
concentration on a ring, bounded H^1 norm outside any surrounding toroid, and
growth of the global H^1 norm with the log-log rate. Analogous behaviour occurs
in any higher dimension. That is, there exists data for which the corresponding
evolution by cubic NLS explodes on a set of co-dimension two. To simplify the
exposition, the proof is presented in dimension three, with remarks to indicate
the adaptations in higher dimension.
