A three-dimensional adaptive grid MHD simulation of the solar wind interaction with comet Halley shows that the boundary of the diamagnetic cavity is a closed, well defined surface. On this surface magnetic field neutral points should exist, and indeed, two O-type neutral points were found at the cavity boundary. In addition, the transition from closed magnetic field lines around the diamagnetic cavity to open field lines in the comet tail requires the formation of at least one X-type neutral point. Such a neutral point was also found in the simulated cometary ionosphere downstream from the cavity. The results of numerical simulations show that the plasma density near the neutral points increases significantly. This increase seems to be indicative of plasma escape from the diamagnetic cavity in the neighborhood of the neutral points, resulting in plasma jets. ¿ 2000 American Geophysical Union