  We construct a smooth gauge for the adjoint field which is free of
ambiguities on the lattice. In this Laplacian Center Gauge, center vortices and
monopoles appear together as local gauge defects. A numerical study of center
vortices in SU(2) and SU(3) supports equality of the $Z_N$ and SU(N) string
tensions in the continuum limit, and only then.
