We investigate the global properties of magnetic reconnection at the dayside terrestrial magnetopause under generic northward interplanetary magnetic field (IMF) conditions. In particular, we consider a zero dipole tilt case where the y and z components of the IMF (in GSM coordinates) are equal in magnitude, using three-dimensional resistive magnetohydrodynamics (MHD) simulations to address the following questions: (1) What is the geometry of the dayside X line? (2) How is current density distributed over the magnetopause surface? Using a technique described by Geene (1992) to track the magnetic nulls in the system, we identify the dayside X line as a magnetic separator line, a segment of a magnetic field line which extends across the dayside magnetopause, terminating in the cusps. We demonstrate that the separator line is the intersection of two separatrix surfaces which define volumes containing topologically distinct field lines. Parallel current density, proportional to the parallel electric field in our resistive MHD simulations, is distributed in a broad, thin sheet which extends across the separator line and terminates in the cusps. Thus separator reconnection at the dayside magnetopause displays features of both antiparallel (near the cusp nulls) and component (near the subsolar separator line) reconnection. We discuss some implications of our results for spacecraft observations of reconnection signatures.