Scattering in H1 for the intercritical NLS with an inverse-square potential

We study the nonlinear Schrödinger equation with an inverse-square potential in dimensions 3≤d≤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 H1 for arbitrary data.