  Spatial Kerr solitons, typically associated with the standard paraxial
nonlinear Schroedinger equation, are shown to exist to all nonparaxial orders,
as exact solutions of Maxwell's equations in the presence of vectorial Kerr
effect. More precisely, we prove the existence of azimuthally polarized,
spatial, dark soliton solutions of Maxwell's equations, while exact linearly
polarized (2+1)-D solitons do not exist. Our ab initio approach predicts the
existence of dark solitons up to an upper value of the maximum field amplitude,
corresponding to a minimum soliton width of about one fourth of the wavelength.
