  We study the fluctuation conductivity of a superconducting film, which is
placed to perpendicular non-uniform magnetic field with the amplitude $H_0$
induced by the ferromagnet with domain structure. The conductivity tensor is
shown to be essentially anisotropic. The magnitude of this anisotropy is
governed by the temperature and the typical width of magnetic domains $d$. For
$d\ll L_{H_0}=\sqrt{\Phi_0/H_0}$ the difference between diagonal fluctuation
conductivity components $\Delta\sigma_\parallel$ along the domain walls and
$\Delta\sigma_\perp$ across them has the order of $(d/L_{H_0})^4$. In the
opposite case for $d\gg L_{H_0}$ the fluctuation conductivity tensor reveals
effective dimensionality crossover from standard two-dimensional $(T-T_c)^{-1}$
behavior well above the critical temperature $T_c$ to the one-dimensional
$(T-T_c)^{-3/2}$ one close to $T_c$ for $\Delta\sigma_\parallel$ or to the
$(T-T_c)^{-1/2}$ dependence for $\Delta\sigma_\perp$. In the intermediate case
$d\approx L_{H_0}$ for a fixed temperature shift from $T_c$ the dependence
$\Delta\sigma_\parallel(H_0)$ is shown to have a minimum at $H_0\sim\Phi_0/d^2$
while $\Delta\sigma_\perp(H_0)$ is a monotonically increasing function.
