  In this paper, the Choquard equation with an inverse-square potential and
both focusing and defocusing nonlinearities in the energy-subcritical regime is
investigated. For all the cases, the local well-posedness result in
$H^1(\mathbb{R}^N)$ is established. Moreover, the global existence result for
arbitrary initial values is proved in the defocusing case while a global
existence/blowup dichotomy below the ground state is established in the
focusing case.
