  We consider finite time blowup solutions of the $L^2$-critical cubic focusing
nonlinear Schr\"odinger equation on $\R^2$. Such functions, when in $H^1$, are
known to concentrate a fixed $L^2$-mass (the mass of the ground state) at the
point of blowup. Blowup solutions from initial data that is only in $L^2$ are
known to concentrate at least a small amount of mass. In this paper we consider
the intermediate case of blowup solutions from initial data in $H^s$, with $1 >
s > s_Q$, where $s_Q \le \sQ$. Our main result is that such solutions, when
radially symmetric, concentrate at least the mass of the ground state at the
origin at blowup time.
