  We study the nonlinear Schr\"odinger equation with an inverse-square
potential in dimensions $3\leq d \leq 6$. We consider both focusing and
defocusing nonlinearities in the mass-supercritical and energy-subcritical
regime. In the focusing case, we prove a scattering/blowup dichotomy below the
ground state. In the defocusing case, we prove scattering in $H^1$ for
arbitrary data.
